Show that d/dx (1+cos 2x/1-cos 2x) = -2 cotx cosec^2 x

I'm thinking that I need to use cos 2x = cos^2 x - sin^2 x, but when? Before or after differentiating? I tried both and just made a big mess. I realise this question is probably easier than it seems but I'm just not seeing it.

Thank you.