Trigonometry! #11

Geometry Level 4

Points $D$ and $E$ are taken on the side $BC$ of $\Delta ABC$ such that $BD=DE=EC$ . If $\angle BAD = x$ , $\angle DAE = y$ , $\angle EAC = z$ , then the value of $\frac {\sin (x+y) \sin (y+z)}{\sin x \sin z}$ is

This problem is part of the set Trigonometry.