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

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The number of all possible values of \( \theta \), where \( 0\theta\pi \), for which the system of equations
[IIT JEE-2010]
\( (y+z) \cos 3 \theta=(x y z) \sin 3 \theta \)
P
W
\( x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} \)
(xyz) \( \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta \) have a solution
\( \left(\mathrm{x}_{0}, \mathrm{y}_{0}, \mathrm{z}_{0}\right) \) with \( \mathrm{y}_{0} \mathrm{z}_{0} \neq 0 \), is
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