Consider the system of equations in x,y,z as xsin3θ-y+z=0,xcos2θ+4y+3z=02x+7y+7z=0 . If this system has a non-trivial solution, then  for integer  n,  values of θ are given by

Given system of equations is xsin3θ−y+z=0xcos2θ+4y+3z=02x+7y+7z=0 are homogeneous system of linear equationsSince the system has non trivial solution∴sin3θ−11cos2θ43277=0sin3θ[28−21]+1[7cos2θ−6]+[7cos2θ−8]=03sinθ−4sin3θ+21−2sin2θ−2=0sinθ4sin2θ+4sinθ−3=0 Either sinθ=0 or 4sin2θ+6sinθ−2sinθ−3=0⇒ (2sinθ−1)(2sinθ+3)=0∴ sinθ=12,sinθ≠−32∴ θ=nπ or θ=nπ+-1nπ6⇒ θ=πn+(−1)n6