How many values of θ with 0° ≤ θ < 360° satisfy 3si$n^2$θ − sinθ − 2 = 0?

Factorising: (3sinθ + 2)(sinθ − 1) = 0. The root sinθ = 1 gives exactly one angle, θ = 90°, because the sine touches its maximum only once per turn. The root sinθ = −2/3 gives two angles, one in the third and one in the fourth quadrant (θ ≈ 221.8° and θ ≈ 318.2°). Total: 3 values.