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