The number of values of $\theta $ $ \in $ (0, $\pi $) for which the system of linear equations x + 3y + 7z = 0 $-$ x + 4y + 7z = 0 (sin3$\theta $)x + (cos2$\theta $)y + 2z = 0. has a non-trival solution, is -

Question

The number of values of $\theta $ $ \in $ (0, $\pi $) for which the system of linear equations

x + 3y + 7z = 0

$-$ x + 4y + 7z = 0

(sin3$\theta $)x + (cos2$\theta $)y + 2z = 0.

has a non-trival solution, is -