How many values of θ with 0° < θ < 360° satisfy 2co$s^2$θ + cosθ − 1 = 0?

Factorising gives (2cosθ − 1)(cosθ + 1) = 0. cosθ = 1/2 gives θ = 60° and θ = 300°; cosθ = −1 gives θ = 180°. That is 3 values in the given range.