2sin2θ+cosθ=1,
2-2cos2θ+cosθ-1=0,
2cos2θ-cosθ-1=0=(2cosθ+1)(cosθ-1), so cosθ=-½ or 1.
cosine is negative in the second and third quadrants.
So θ=180-60=120°, and 180+60=240°. cosθ=1 when θ=0°.
More generally, θ=360n+120 degrees, 360n+240 degrees, 360n degrees, where n is an integer (positive or negative).