Let θ ∈(0, (π)/2). If the system of linear equations. (1+ cos^2 θ) x+ sin^2 θ y+4 sin 3 θ z=0; cos^2 θ x+(1+ sin^2 θ) y+4 sin 3 θ z=0; cos^2 θ x+…

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