Matrices and Determinants

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_\limits{\theta \in \mathrm{s}} \theta is equal to :