The number of all possible values of

MATHEMATICS · Subjective · ISC · Mathematics · Algebra (Matrices and Determinants) · Systems of linear equations

Problem

The number of all possible values of θ\theta , where 0<θ<π0 < \theta < \pi , for which the system of equations (y+z)cos⁡3θ=(xyz)sin⁡3θ(y+z) \cos 3\theta = (xyz) \sin 3\theta xsin⁡3θ=2cos⁡3θy+2sin⁡3θzx \sin 3\theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z} and (xyz)sin⁡3θ=(y+2z)cos⁡3θ+ysin⁡3θ(xyz) \sin 3\theta = (y+2z) \cos 3\theta + y \sin 3\theta have a solution (x0,y0,z0)(x_0, y_0, z_0) with y0z0≠0y_0 z_0 \neq 0 , is .....

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