The set $S$ is all values of $\theta\in[-\pi,\pi]$ for which the system $x+y+\sqrt{3},z=0,\quad -x+(\tan\theta),y+\sqrt{7},z=0,\quad x+y+(\tan\theta),z=0$ has a non-trivial solution. Then $\dfrac{120}{\pi}\displaystyle\sum_{\theta\in S}\theta$ is equal to: