Points \( D, E \) are taken on the side \( B C \) of a triangle \( A B C \), such that \( B D=D ...

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Points \( D, E \) are taken on the side \( B C \) of a triangle \( A B C \), such that \( B D=D E=E C \). If \( \angle B A D=x, \angle D A E=y, \angle E A C=z \), then the value of \( \frac{\sin (x+y) \sin (y+z)}{\sin x \sin z} \) is equal to
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