Using the half/double angle formulas to solve an equation I am completely stumped by this problem: $$\cos\theta - \sin\theta =\sqrt{2} \sin\frac{\theta}{2} $$
I know that I should start by isolating $\sin\dfrac{\theta}{2}$
and end up with $$\frac {\cos\theta - \sin\theta}{\sqrt{2}} = \sin\frac{\theta}{ 2}$$
From here on out, I have no idea what steps to take.

$$\cos \theta . \sin \frac{\pi}{4} - \cos \frac{\pi}{4} . \sin \theta = \sin \frac{\theta}{2}$$
$$\sin (\frac{\pi}{4} - \theta) = \sin \frac{\theta}{2}$$
$$\frac{\pi}{4} - \theta = n\pi + (-1)^n(\frac{\theta}{2})$$
