find to the nearest minute, all positive values in the interval 0° ≤ θ < 180° that satisfy the equation 2 tan^2 θ - tan θ = 3
Let x = tanθ
You have a quadratic equation in x
2x^2 -x -3 = 0
(2x -3)(x+1) = 0
x = tanθ = -1 or 3/2
θ = 135 degrees or 56.3099 degrees
The latter angle is 56 degrees 19 minutes