More generally, we have
[tex](a-b)^2-(a+b)^2=(a^2-2ab+b^2)-(a^2+2ab+b^2)=-4ab[/tex]
so that
[tex](\sin\theta-\cos\theta)^2-(\sin\theta+\cos\theta)^2=-4\sin\theta\cos\theta=-2\sin2\theta[/tex]
