Решите уравнение: \(2 sin^2 \frac{x}{2} + \frac{1}{2}sin 2x = 1.\)

• \(\frac{\pi}{2} + \pi n, n \in Z\)
• \(\frac{\pi}{2} + 2\pi n, n \in Z\)
• \(\frac{\pi}{4} + \pi n, n \in Z\)