I entered your identity in the Google search window and got all kind of solutions.
Here are the first two:
https://in.answers.yahoo.com/question/index?qid=20140221115147AA0ejyo
http://www.meritnation.com/ask-answer/question/prove-that-tana-2tan-2a-4tan4a-8cot8a-cota/trigonometric-functions/1500948
Prove: TanA+2Tan2A+4Tan4A+8Cot8A=CotA
1 answer