The number of all possible values of $\theta$ where $0 < \theta < \pi$ for which the system of equations $(y+z)\cos 3\theta=(xyz)\sin 3\theta$,$x\sin 3\theta=\large\frac{2\cos 3\theta}{y}+\frac{2\sin 3\theta}{z}$,$(xyz)\sin 3\theta=(y+2z)\cos 3\theta+y\sin 3\theta$ have a solution $(x_0,y_0,z_0)$ with $y_0,z_0\neq 0$ is

Question

$\begin{array}{1 1}(a)\;4&(b)\;5\\(c)\;2&(d)\;3\end{array}$