If $C=2\cos \theta$ then the value of the determinant $4\Delta=\begin{vmatrix}c&1&0\\1&c&1\\0&1&c\end{vmatrix}$ is

Question

$\begin{array}{1 1}(A)\;\large\frac{\sin 4\theta}{\sin \theta}&(B)\;\large\frac{2\sin ^2\theta}{\sin \theta}\\(C)\;4\cos^2\theta(2\cos \theta-1)&(D)\;\text{None }\end{array}$