Solve `4cot2theta=cot^2theta-tan^2theta`

Explanation

`4/(tan 2 theta)=1/(tan^(2) theta)-tan^(2) theta`
or `(4(1-tan^(2) theta))/(2 tan theta)=(1- tan^(4) theta)/(tan^(2) theta)" "["put "tan 2 theta=(2 tan theta)/(1-tan^(2) theta)]`
or `(1-tan^(2) theta)[2 tan theta-(1+tan^(2) theta)]=0`
or `(1-tan^(2) theta)(tan^(2) theta-2 tan theta+1)=0`
or `(1-tan^(2) theta) (tan theta-1)^(2) =0`
or `tan theta= pm 1`
`rArr theta= n pi pm pi/4, n in Z`