The number of all possible values of \( \theta \), where \( 0\theta \) \( \pi \), for which the ...

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The number of all possible values of \( \theta \), where \( 0\theta \) \( \pi \), for which the system of equations \( (y+z) \cos 3 \theta \) \( =(x y z) \sin 3 \theta ; x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} ;(x y z) \) \( \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta \) have a solution \( \left(x_{0}, y_{0}\right. \), \( z_{0} \) ) with \( y_{0} z_{0} \neq 0 \), is
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