Let \(\theta \in\left(0, \frac{\pi}{2}\right)\). If the system of linear equations. \(\begin{aligned}& \left(1+\cos ^2 \…

Let \(\theta \in\left(0, \frac{\pi}{2}\right)\). 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 \(\theta\) is:

[JEE Main 2021, 26 Aug (Shift 1)]