Prove that the left equals the right

$\displaystyle 1-(sin^2x)/(1+cotx)-(cos^2x)/(1+tanx) = sin2x/2$

So far I've multiplied to get a common denominator of $\displaystyle 1+tanx+cotx+cotxtanx$ And have the numerator of $\displaystyle cotx+tanx+cotxtanx$ Past this I can't think of where to go.