Let \(S\) be the set of all values of \(\theta \in[-\pi, \pi]\) for which the system of linear equations \(\begin{aligne…

Let \(S\) be the set of all values of \(\theta \in[-\pi, \pi]\) for which the system of linear equations
\(\begin{aligned}& x+y+\sqrt{3} z=0 \\& -x+(\tan \theta) y+\sqrt{7} z=0\\&x+y+(\tan \theta) z=0
\end{aligned}\)
has non-trivial solution. Then \(\frac{120}{\pi} \sum_{\theta \in s} \theta\) is equal to

[JEE Main 2023, 8 Apr (Shift 2)]