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The number of all possible values of θ w...

The number of all possible values of θ where 0 < θ < π, for which the system of equations `(y + z)cosθ = (xyz)sin3θ`
`sin3θ = 2cos((3θ)/y )+ 2sin((3θ)/z)`
`(xyz)sin3θ = (y + 2z)cos3θ + ysin3θ`
has a solution `(x_0,y_0,z_0) ` with `y_0 ,z_0 ≠ 0,` is

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