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 \(\det A=0\).