limits - Find: $lim_{xto frac{pi}{4}} frac{sin 4x}{1-sqrt{2} cos x}$ (no L'Hopital)

Find: $\displaystyle \lim_{x\to \frac{\pi}{4}} \frac{\sin 4x}{1-\sqrt{2} \cos x}$ (no L'Hopital)

By L'Hopital it is easy to show that this limit is $-4$. But I'm not finding the right approach to prove without using it.

Hints and answers appreciated. Sorry if this is a duplicate.