If $C=2\cos \theta$ then the value of the determinant $\Delta=\begin{vmatrix}c&1&0\\1&c&1\\6&1&c\end{vmatrix}$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{2\sin^2\theta}{\sin \theta}&(b)\;8\cos^3\theta-4\cos\theta+6\\(c)\;\large\frac{2\sin 2\theta}{\sin \theta}&(d)\;8\cos^3\theta+4\cos \theta+6\end{array}$