Question

The number of all possible values of θ where 0 < θ < π, for which the system of equations

(y + z)cosθ = (xyz)sin3θ

sin3θ = 2cos3θ/y + 2sin3θ/z

(xyz)sin3θ = (y + 2z)cos3θ + ysin3θ

has a solution (x₀,y₀,z₀) with y₀z₀  ≠ 0,  is

Answer 1

We have

By Eqs. (1), (2), & (3)