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 :

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 :

${{4\pi } \over 9}$

${{7\pi } \over {18}}$

${\pi \over {18}}$

${{5\pi } \over {18}}$

Solution

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