Cot(2X) - Cot(3X) = 1/2SecXCsc(3X)

Here are the Identities I (read: You) have to work with

cscX = 1/sinX

secX = 1/cosX

cotX = 1/tanX

tanX = sinX/cosX

cotX = cosX/sinX

sin(x+y) = sinXcosY + cosXsinY

sin(x-y) = sinXcosY - cosXsinY

cos(x+y) = cosXcosY - sinXsinY

cos(x-y) = cosXcosY + sinXsinY

tan(x+y) = tanX+tanY/1-tanXtanY

tan(x-y) = tanX-tanY/1+tanXtanY

cos2X = (cos(X))^2 - (sin(x))^2

cos2X = 1-2(sin(x))^2

cos2X = 2(cos(x))^2 - 1

sin2X = 2sinXcosX

tan2X = 2tanX/1- (tan(x))^2