Show that: $$\sin ^2 (a+b)+\sin ^2 (a-b)=4(1-\cos ^2 a \cos ^2 b)$$

I tried two approaches.

Approach 1: $$\sin ^2 (a \pm b)=\sin a\cos b \pm \sin b\cos a$$

This reduced to: $$2(\cos ^2 a +\cos ^2 b -2\cos ^2 a\cos ^2b)$$

I can't see where to go from here.

Approach 2: $$\sin ^2 (a \pm b)=1-\cos ^2 (a \pm b)$$

This reduced to: $$2(\cos ^2 a +\cos ^2 b -2\cos ^2 a\cos ^2b)$$

Both approaches reduced to the same expression which is a good sign, but I still can't figure out how to make the final manipulation.