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 :