The number of all possible values of $\theta$ where $0 \lt \theta \lt \pi ,$ for which the system of equations $\left( {y + z} \right)\cos {\mkern 1mu} 3\theta = \left( {xyz} \right){\mkern 1mu} \sin 3\theta x\sin 3\theta = {{2\cos 3\theta } \over y} + {{2\sin 3\theta } \over z}\left( {xyz} \right){\mkern 1mu} \sin 3\theta = \left( {y + 2z} \right){\mkern 1mu} \cos 3\theta + y{\mkern 1mu} sin3\theta$ have a solution $$\left( {{x_0},{y_0},{z_0}} \right)$$ with ${y_0}{z_0}{\mkern 1mu} e {\mkern 1mu} 0,$ is