trigonometry - Verify identity: $sin(x+1)sin(x+1) - sin(x+2)sin x = sin^2(1)$

I have the following identity to verify:
$$\sin(x+1)\sin(x+1) - \sin(x+2)\sin x = \sin^2(1).$$

I'm becoming more familiar with sum and difference formulas to some degree, but this one has stumped me.

I don't know if I'm doing it right, even, but I have this so far:
$$(\sin x \cos(1) + \cos x \sin(1))^2 - (\sin x \cos(2) + \cos x \sin(2))(\sin x) = \sin^2(1). $$

I don't want to just ask "how i do dis" and expect an answer. I am trying, but my brain doesn't quite understand all this yet.

Please help! I may be late to reply, I have work to get to here.

Thanks a million,

-Jon