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.

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