The number of values of θ with 0° ≤ θ < 360° for which sin3θ = 0 is:

sin3θ = 0 means 3θ is a whole multiple of 180°. As θ sweeps [0°, 360°), the angle 3θ sweeps [0°, 1080°), which contains 0°, 180°, 360°, 540°, 720° and 900° — six multiples. Dividing back gives θ = 0°, 60°, 120°, 180°, 240°, 300°. Solving only within one turn of 3θ gives the trap 3.