Question 73
Let $ABCD$ be a cyclic quadrilateral, and let segments $AC$ and $BD$ intersect at $E$. Let $W$ and $Y$ be the feet of the altitudes from $E$ to sides $DA$ and $BC$, respectively, and let $X$ and $Z$ be the midpoints of sides $AB$ and $CD$, respectively. Given that the area of $AED$ is $9$, the area of $BEC$ is $25$, and $\angle EBC - \angle ECB = 30^{\circ}$, then compute the area of $WXYZ$.