Case 1: sin(3θ)=cos(2θ)=1,0≤θ≤2π.sin(3θ)=1⟹3θ=2π+2πk⟹θ=6π+32πk.θ=6π,65π,23π(1)cos(2θ)=1⟹2θ=2πk⟹θ=πk.θ=0,π,2π(2) From (1) and (2), there is no common θ.
Case 2: sin(3θ)=cos(2θ)=−1,0≤θ≤2π.sin(3θ)=−1⟹3θ=23π+2πk⟹θ=2π+32πk.θ=2π,67π,611π(3)cos(2θ)=−1⟹2θ=π+2πk⟹θ=2π+πk.θ=2π,23π(4) By (3) and (4), the common angle is θ=2π.