2\sin2θ=1+\cosθ
2(1−\cos2θ)=1+\cosθ
2−2\cos2θ=1+\cosθ
0=1−2+\cosθ+2\cos2θ
2\cos2θ+\cosθ−1=0
Factorizing, we have
(\cosθ+1)(2\cosθ−1)=0
Note: In the range, 0°≤θ≤90°, all trig functions are positive, so we consider
2\cosθ=1implies\cosθ=12
θ=60°.