The sum of all values of θ in 0° ≤ θ ≤ 90° that satisfy 2si$n^2$θ − 3sinθ + 1 = 0 is:

Factorising gives (2sinθ − 1)(sinθ − 1) = 0, so sinθ = 1/2 or sinθ = 1. In the given range that means θ = 30° and θ = 90°, whose sum is 120°. Forgetting the root sinθ = 1 leaves only 30°.