HMMT November 2022 U4

Let $A B C D$ be a square of side length 2 . Let points $X, Y$, and $Z$ be constructed inside $A B C D$ such that $A B X, B C Y$, and $C D Z$ are equilateral triangles. Let point $W$ be outside $A B C D$ such that triangle $D A W$ is equilateral. Let the area of quadrilateral $W X Y Z$ be $a+\sqrt{b}$, where $a$ and $b$ are integers. Find $a+b$.