If `x+y+z=pi/2,` then prove that `|[sinx,siny,sinz],[cosx,cosy,cosz],[cos^3x,cos^3 y,cos^3z]|=0`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
\sin x & \sin y & \sin z \\
\cos x & \cos y & \cos z \\
\cos^3 x & \cos^3 y & \cos^3 z
\end{array} \right| = 0
...