In the range 0° ≤ θ ≤ 180°, the solution set of 2co$s^2$θ − 5sinθ + 1 = 0 is:

Replace co$s^2$θ by 1 − si$n^2$θ: 2 − 2si$n^2$θ − 5sinθ + 1 = 0, i.e. 2si$n^2$θ + 5sinθ − 3 = 0, which factorises as (2sinθ − 1)(sinθ + 3) = 0. Only sinθ = 1/2 is possible, and between 0° and 180° that gives both θ = 30° and its supplement θ = 150°. Missing the supplement leaves {30°}, and 210° is outside the stated range.