Apart from 20° itself, the only angle θ with 0° ≤ θ < 360° for which sinθ = sin20° is:

The sine takes equal values at an angle and at its supplement, so sin160° = sin(180° − 20°) = sin20° ≈ 0.342. The angles 200° and 340° give −0.342 — the same size but the wrong sign, since the sine is negative below the axis — and sin110° = cos20° ≈ 0.940, a different number altogether. Within one turn the sine repeats a given positive value exactly twice, so 20° and 160° are the complete list.