The sum of all possible values of \(\theta \in[0,2 \pi]\), for which the system of equations: \( x \cos 3 \theta-8 y-12 …

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

\( x \cos 3 \theta-8 y-12 z=0 \)

\( x \cos 2 \theta+3 y+3 z=0 \)

\( x+y+3 z=0\)

has a non-trivial solution, is equal to:

[JEE Main 2026, 6 Apr (Shift 2)]