Question 99
Let $ABCD$ be a square of side length $2$. Let points $X$, $Y$, and $Z$ be constructed inside $ABCD$ such that $ABX$, $BCY$, and $CDZ$ are equilateral triangles. Let point $W$ be outside $ABCD$ such that triangle $DAW$ is equilateral. Let the area of quadrilateral $WXYZ$ be $a + \sqrt{b}$, where $a$ and $b$ are integers. Find $a + b$.