HMMT 2020 U26

Let $A B C D$ be a cyclic quadrilateral, and let segments $A C$ and $B D$ intersect at $E$. Let $W$ and $Y$ be the feet of the altitudes from $E$ to sides $D A$ and $B C$, respectively, and let $X$ and $Z$ be the midpoints of sides $A B$ and $C D$, respectively. Given that the area of $A E D$ is 9 , the area of $B E C$ is 25 , and $\angle E B C-\angle E C B=30^{\circ}$, then compute the area of $W X Y Z$.