The next Live Letter, with Part 2 of the patch 3.3 info, will be on May 22nd, so we know that it’s no earlier than that (that’s probably also when we’ll be told the official release date).

That said, the average time between major (e.g. x.1 and x.2) patches since 2.0 has been 114 days (16.3 weeks or 3.7 months). 114 days after 3.1 would be Thursday, June 16th, but all the recent major patches have been on a Tuesday (to coincide with the weekly reset), so June 7th and June 14th are plausible guesses if they stay on their normal pace.

Even if you discount the long delay between 3.0 and 3.1 as an anomaly, the average only drops to 110 days, which would be June 12th, so likely the same projection.