Let \( y = y(x) \) be the solution of the differential equation \( 2\cos x \dfrac{dy}{dx} = \sin 2x - 4y \sin x, \; x \in \left(0,\dfrac{\pi}{2}\right). \) If \( y\!\left(\dfrac{\pi}{3}\right)=0 \), then \( y'\!\left(\dfrac{\pi}{4}\right) + y\!\left(\dfrac{\pi}{4}\right) \) is equal to \( \underline{\phantom{xxxx}} \).
