Why does the Underworld team release their movies exactly with 3 years gaps?

Based on this article, it's likely just a function of market research:

It got us thinking: Is there an ideal amount of time that should pass between sequels to maximize the box office? To find out, we studied every modern-day live-action franchise that met the following criteria: The series had to span at least three movies, it had to retain most of its original cast or its director, and the first film needed to come out in 1990 or later (to limit the effect of inflation). What did we discover?

The Sweet Spot: Sequels that come out every two to four years. Time and time again in our research, we found the best results from franchises that allow an average of three years' breathing room between installments—just enough time for a series to grow in people's minds and to find an even bigger audience on home video. Three years went by between the main movies in the X-Men series (not counting spinoffs) and the Austin Powers series, and each sequel bettered the last, often by a significant amount. Two years passed before the second Bourne movie outgrossed the first by more than $50 million, then three years passed before the third movie pulled the same trick, improving on the original by over $100 million.

The entire article does a pretty good analysis showing most film franchises in the last two decades and their prospective revenues.

Of course you also have to factor in high rating stars being on other projects, renegotiations, writing delays, etc.

Note that Underworld: Blood Wars (previously known as Underworld: Next Generation) started production in October 2015, and was slated for October 2016 release, breaking the 3 years between sequels pattern. It actually came out January 2017 (Internationally November 2016). Underworld 6 is still planned but no dates given yet. Let's bet it's 2020.