Matrices And Determinants

The sum of all possible values of $\theta \in[0,2 \pi]$, for which the system of equations :

$$ \begin{aligned} & x \cos 3 \theta-8 y-12 z=0 \\ & x \cos 2 \theta+3 y+3 z=0 \\ & x+y+3 z=0 \end{aligned} $$

has a non-trivial solution, is equal to :