The number of all possible values of θ, where 0<θ<π, for which the – InterviewSolution

1.	The number of all possible values of θ, where 0<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) with y0z0≠0, is
Answer» The number of all possible values of $θ$ , where $0 < θ < π$ , for which the system of equations $(y + z) cos 3 θ = (x y z) sin 3 θ$ $x sin 3 θ = \frac{2 cos 3 θ}{y} + \frac{2 sin 3 θ}{z}$ $(x y z) sin 3 θ = (y + 2 z) cos 3 θ + y sin 3 θ$ have a solution $(x_{0}, y_{0}, z_{0})$ with $y_{0} z_{0} \neq 0$ , is

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