The value of θfor which the system sin3θx−y+z=0, cos2θx+4y+3z=0, 2x+7y+7z=0 has a non-trivial solution is   (where π2<θ<π,(π=3.14))

The system has non-trivial solution, ifsin3θ-11cos2θ43277=0⇒sin3θ(7)+cos2θ(14)+2(-7)=0⇒sin3θ=2(1-cos2θ)⇒sinθ3-4sin2θ=4sin2θ⇒4sin2θ+4sinθ-3=0⇒(2sinθ-1)(2sinθ+3)=0⇒sinθ=12;sinθ=-32 (No solution). ⇒θ=5π6   ∵θ∈(π/2,π)       =2.617.