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The number of all possible values of the...

The number of all possible values of `theta`, where `0 lt theta lt pi`, for which the system of equations
`(y+z) cos 3 theta = (xyz) sin 3 theta`
`x sin 3 theta=(2 cos 3 theta)/y+(2 sin 3 theta)/z`
`(xyz) sin 3 theta = (y+2z) cos 3 theta +y sin 3 theta`
has a solution `(x_(0), y_(0), z_(0))` with `y_(0)z_(0) ne 0` is _______.

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