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