(See) Let
Question: Let
\[A=\left[ \begin{matrix} \sin x & \cos x & \sin \left( x+a \right) \\ \sin y & \cos y & \sin \left( y+a \right) \\ \sin z & \cos z & \sin \left( z+a \right) \\ \end{matrix} \right]\]Without directly evaluating \(\det A\), prove that \(\det A=0\).
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