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The long-awaited moment has arrived: Britain finally has submitted its declaration of independence from the European Union (if you're a Leave supporter) or has confirmed in writing that it wants to go ahead with one of the biggest mistakes in its history (if you're a Remain supporter).

Whatever the investor's take on this, the only thing that became certain from the moment Prime Minister Theresa May's letter was delivered is uncertainty.

The words of European Council President Donald Tusk should serve as a warning about what is ahead: "There is nothing to win for both sides. This is about damage control. Our goal is clear -- to minimize the cost for EU citizens, businesses and member states. We will do everything in our power and we have all the tools to achieve this goal."

Ever since the vote last June, the U.K. politicians' tactics have been to try to divide the remaining 27 EU members, helped by the anti-EU stance of President Donald Trump after he was elected. However, paradoxically, Brexit could serve as a catalyst for the rest of the EU, and especially for the 19-member eurozone, to pull together.

Signs of that unity became prominent earlier this week, before the U.K. triggered the EU Treaty's Article 50. The eurozone break-up index compiled by the Frankfurt-based Sentix Institute, which specializes in behavioral finance, showed that fears of an implosion calmed down significantly after the mid-month general elections in the Netherlands.

The extremist, anti-EU Freedom Party of Geert Wilders failed to become the biggest party in the Dutch parliament despite months of polls showing it ahead in voters' preferences. This outcome prompted investors to "reconsider their pessimism about the union," in the words of Manfred Huebner, managing director of the Sentix Institute.

The Sentix euro break-up index fell to 18.7% in March. It was the first time since last October that the index, which measures the probability that a member country exits the single currency area, fell below 20%.

The probability of a break-up by one of the "threatening three" -- as the Sentix Institute called the Greek, French and Italian sub-indices because they showed higher probabilities of a break-up than elsewhere -- fell significantly. Greece led the way, with the exit probability dropping to 13% in March from 19% in February.

The reality is that even in the hardest-hit European countries, trust in the EU has been recovering since the debt crisis of 2010-2012. Analysis by the Brussels-based Bruegel think tank shows that for Portugal, Italy, Greece and Spain -- the infamous "PIGS" -- trust in the EU and support for the euro have been on the rise since 2013.

Besides improving sentiment, eurozone equities also benefit from "reasonable valuation," according to analysts at Societe Generale who say the asset class trades on a forward price/earnings multiple of 14.5x vs. a 17-year average of 13.6x. Stocks in the single currency area also could get a boost from a reassessment of expectations regarding the tapering of the European Central Bank's easy monetary policy.

Reuters reported that one source close to the ECB's Governing Council said the central bank's March 9 statements have been over-interpreted as being less dovish. This statement helped to send the euro lower versus the dollar on Wednesday.

"We wanted to communicate reduced tail risk, but the market took it as a step to the exit," the source said. "The message was way over-interpreted."

If that is indeed the case -- and recent data showing inflation may have peaked seems to confirm the ECB would be justified to remain dovish -- then eurozone stocks have much more runway. The ECB's easy policy would stimulate the economy further and a weaker euro would attract foreign investors eager to take advantage of cheaper prices.

U.S. investors seeking general exposure to the single European area can take a look at the iShares MSCI EMU Index ETF (EZU) - Get Report , a capitalization-weighted ETF that seeks to capture 85% of the total market capitalization of equities in the area.

Another ETF offering wide exposure is the Deutsche X-trackers MSCI Eurozone Hedged Equity ETF (DBEZ) - Get Report , which tracks an index of stocks from eurozone members and hedges against euro-dollar currency fluctuations. It aims to capture 99% of the eurozone market by including small caps.

There is also the WisdomTree Europe Hedged Equity Fund (HEDJ) - Get Report , which is hedged as well. One drawback could be that this ETF targets eurozone dividend-paying companies that get at least 50% of their revenue from exports outside the single currency area. While that's a good thing in times of eurozone weakness, it could weigh on the results as the eurozone keeps growing.

Amid the uncertainty unleashed by Brexit, investors are likely to find good eurozone opportunities for the long term. The French presidential elections in late April and early May are likely to cause another wobble in the markets, as are the German general elections in late September.

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