The number of $\theta \in(0,4 \pi)$ for which the system of linear equations $$ \begin{aligned} &3(\sin 3 \theta) x-y+z=2 \\\\ &3(\cos 2 \theta) x+4 y+3 z=3 \\\\ &6 x+7 y+7 z=9 \end{aligned} $$ has no solution, is :

Question

The number of $\theta \in(0,4 \pi)$ for which the system of linear equations

$$ \begin{aligned} &3(\sin 3 \theta) x-y+z=2 \\\\ &3(\cos 2 \theta) x+4 y+3 z=3 \\\\ &6 x+7 y+7 z=9 \end{aligned} $$

has no solution, is :

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