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

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

[JEE Main 2023, 08 Apr (Shift 2)]