The number of values of $\theta \in(0, \pi)$ for which the system of linear equations
$$
\begin{aligned}
& x+3 y+7 z=0 \\
& -x+4 y+7 z=0 \\
& (\sin 3 \theta) x+(\cos 2 \theta) y+2 z=0
\end{aligned}
$$
has a non-trivial solution, is:
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