Let \( y = y(x) \) be the solution of the differential equation \( \sec x \, \frac{dy}{dx} - 2y = 2 + 3\sin x, \; x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \) and \( y(0) = -\frac{7}{4} \). Then \( y\!\left(\frac{\pi}{6}\right) \) is equal to:
