Definite Integration

If \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a continuous function satisfying \(\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0\), then the value of \(\alpha\) is :