JEE Math Practice Question

A value of $$\theta \in \left( {0,{\pi \over 3}} \right)$$, for which $$\left| {\begin{matrix} {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \\ {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \\ {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \\ \end{matrix} } \right| = 0$$, is :

1. A.$${\pi \over {18}}$$
2. B.$${\pi \over {9}}$$
3. C.$${{7\pi } \over {24}}$$
4. D.$${{7\pi } \over {36}}$$