Without expanding, show that the value of each of the following determinants is zero \[ \left|\b...

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Without expanding, show that the value of each of the following determinants is zero
\[
\left|\begin{array}{rrr}
\cos (x+y) & -\sin (x+y) & \cos 2 y \\
\sin x & \cos x & \sin y \\
-\cos x & \sin x & -\cos y
\end{array}\right|
\]
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