The number of values of θ∈ 0,πfor which the system of equations x+3y+7z=0, −x+4y+7z=0, sin3θx+cos2θy+2z=0has a non-trivial solution is

System has non-trivial  solution⇒Δ=0 ⇒137−147sin3θcos2θ2=0 ⇒18-7cos2θ-3-2-7sin3θ+7-cos2θ-4sin3θ=0 ⇒14-14cos2θ-7sin3θ=0 ⇒sin3θ+2cos2θ-2=0 ⇒3sinθ-4sin3θ+21-2sin2θ-2=0 ⇒sinθ4sin2θ+4sinθ-3=0 ⇒sinθ4sin2θ+6sinθ-2sinθ-3=0 ⇒sinθ2sinθ-12sinθ+3=0 ⇒sinθ=0 ,  2sinθ-1=0⇒sinθ=12 ∵θ∈0,π⇒θ=π6,5π6 ⇒The number of values of θ is 2