The value of $\frac{\sin 1^{\circ }+\sin 3^{\circ }+\sin 5^{\circ }+\sin 7^{\circ }}{\cos 1^{\circ }\cdot \cos 2^{\circ }\cdot \sin 4^{\circ }}$is ______.

$\begin{array}{l}\frac{2\sin 4^{\circ }\cos 3^{\circ }+2\sin 4^{\circ }\cos 1^{\circ }}{\cos 1^{\circ }\cos 2^{\circ }\sin 4^{\circ }}\\ =\frac{2\sin 4^{\circ }\left[\cos 3^{\circ }+\cos 1^{\circ }\right]}{\cos 1^{\circ }\cos 2^{\circ }\sin 4^{\circ }}\\ =\frac{4\cos 2^{\circ }\cos 1^{\circ }}{\cos 1^{\circ }\cos 2^{\circ }}=4\end{array}$