Prove $\left|\begin{smallmatrix} \sin^2x&\cot x&1\\ \sin^2y&\cot y&1\\ \sin^2z&\cot z&1 \end{smallmatrix}\right|=0$ if $x+y+z=\pi$

Question

If $x, y, z$ are the angles of $\Delta ABC$, then evaluate

$$ \Delta=\begin{vmatrix} \sin^2x&\cot x&1\\ \sin^2y&\cot y&1\\ \sin^2z&\cot z&1 \end{vmatrix}=\quad\color{red}{?} $$

My Attempt

$$ \Delta=\frac{1}{\sin x\sin y\sin z}\begin{vmatrix} \sin^3x&\cos x&\sin x\\ \sin^3y&\cos y&\sin y\\ \sin^3z&\cos z&\sin z \end{vmatrix}= $$ How do I proceed further and prove that the determinant is zero ?