Let S be the set of all values of θ ∈[-π, π] for which the system of linear equations x+y+√ 3 z=0; -x+( tan θ) y+√ 7 z=0; x+y+( tan θ) z=0 has…

Let $\displaystyle S$ be the set of all values of $\displaystyle \theta \in[-\pi, \pi]$ 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 $\displaystyle \frac{120}{\pi} \sum_{\theta \in \mathrm{s}} \theta$ is equal to