The number of all possible values of $\theta$, where $0 < \theta < \pi$, for which the system of equations
$$\begin{gathered}
( y + z ) \cos 3 \theta = ( x y z ) \sin 3 \theta \\
x \sin 3 \theta = \frac { 2 \cos 3 \theta } { y } + \frac { 2 \sin 3 \theta } { z } \\
( x y z ) \sin 3 \theta = ( y + 2 z ) \cos 3 \theta + y \sin 3 \theta
\end{gathered}$$
have a solution $\left( x _ { 0 } , y _ { 0 } , z _ { 0 } \right)$ with $y _ { 0 } z _ { 0 } \neq 0$, is