The number of all possible values of θ,where0<θ<π, for which the sy – InterviewSolution

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1.	The number of all possible values of θ,where0<θ<π, for which the system of equations (y+z)cos3θ=(xyz)sin3θ xsin3θ=2cos3θy+2sin3θz(xyz)sin3θ=(y+2z)cos3θ+ysin3θ have a solution (x0,y0,z0)withy0z0≠0 is___
Answer» The number of all possible values of $θ, w h e r e 0 < θ < π$ , for which the system of equations $(y + z) c o s 3 θ = (x y z) s i n 3 θ$ $x s i n 3 θ = \frac{2 c o s 3 θ}{y} + \frac{2 s i n 3 θ}{z} (x y z) s i n 3 θ = (y + 2 z) c o s 3 θ + y s i n 3 θ$ have a solution $(x_{0}, y_{0}, z_{0}) w i t h y_{0} z_{0} \neq 0$ is___

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