This answer is incorrect!
#cot^4 theta = cos^4 theta/sin^4 theta#
#1-cos^2 theta = sin^2 theta#
Here is where the mistake was made:
#cot^4 theta / (1-cos^4 theta) = (cos^4 theta/sin^4 theta)/(sin^2 theta*cos^2 theta#
#(cos^4 theta/sin^4 theta)/(sin^2 theta*cos^2 theta) = (cos^2 theta/sin^4 theta)/(sin^2 theta)#
#(cos^2 theta/sin^4 theta)/(sin^2 theta/1)# or #cos^2 theta/sin^4 theta*1/sin^2 theta#
Multiply across
#cos^2 theta/sin^6 theta# = #cot^2 theta/sin^4 theta#
Expand to get rid of the exponents
#(cottheta*cottheta)/(sintheta*sintheta*sintheta*sintheta)#
I hope this is the form you were looking for!