Решите уравнение 2sin^2(x) - √3sin(x) - 3 = 0.

Let y = sin(x). The equation becomes 2y^2 - √3y - 3 = 0. Using the quadratic formula, y = (√3 ± √(3 - 4*2*(-3))) / 4 = (√3 ± √27) / 4 = (√3 ± 3√3) / 4. Thus, y = √3 or y = -√3/2. Since -1 ≤ sin(x) ≤ 1, sin(x) = √3 is impossible. Therefore, sin(x) = -√3/2. The general solution is x = -π/3 + 2πn or x = 4π/3 + 2πn, where n is an integer.