We have
∣∣
∣∣11sin3θ−43cos2θ7−7−2∣∣
∣∣=0
Applying C1→C1+C2, we get
∣∣
∣∣21sin3θ−13cos2θ0−7−2∣∣
∣∣=0
Applying R1→R1+2R2
∣∣
∣∣07sin3θ+2cos2θ−13cos2θ0−7−2∣∣
∣∣=0
Expanding along C1, we get
=1[−14+7(sin3θ+2cos2θ]=0
⇒(3sinθ−4sin3θ)+2(1−2sin2θ)−2=0⇒4sin3θ+4sin2θ−3sinθ=0⇒sinθ(4sin2θ+4sinθ−3)=0⇒sinθ(4sin2θ+6sinθ−2sinθ−3)=0⇒sinθ(2sinθ−1)(2sinθ+3)=0⇒sinθ=0 or sinθ=12 or sinθ=−32
⇒sinθ≠−32
∴sinθ=0 or 12
∴ Possible values of θ=0,π,2π,π6,5π6