If the system of linear equations sin 3θx−y+z=0, cos2θx+4y+3z=0 ,  2x+7y+7z=0 has a non-trivial solution then the values of  θ are

Given equations have non zero solution  ⇒sin⁡3θ−11cos⁡2θ43277=0⇒(sin⁡3θ)(28−21)−(cos⁡2θ)(−7−7)+2(−3−4)=0⇒sin⁡3θ+2cos⁡2θ−2=0⇒3sin⁡θ−4sin3⁡θ+21−2sin2⁡θ=2⇒3sin⁡θ−4sin2⁡θ−4sin3⁡θ=0⇒−sin⁡θ4sin2⁡θ+4sin⁡θ−3=0⇒sin⁡θ(2sin⁡θ+3)(2sin⁡θ−1)=0⇒sin⁡θ=0 or sin⁡θ=1/2⇒θ=nπ or θ=nπ+(−1)nπ/6,n∈Z