JEE Math Practice Question

Let $$\theta \in \left( {0,{\pi \over 2}} \right)$$. If the system of linear equations $$(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0$$ $${\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0$$ $${\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0$$ has a non-trivial solution, then the value of $$\theta$$ is :

1. A.$${{4\pi } \over 9}$$
2. B.$${{7\pi } \over {18}}$$
3. C.$${\pi \over {18}}$$
4. D.$${{5\pi } \over {18}}$$