Question

cot.alpha+cot(60+alpha)-cot(60-alpha)=3cot3alpha

Answer 1

see

http://www.askiitians.com/forums/Trigonometry/prove-cot-a-cot-60-a-cot-60-a-3-cot3a_106221.htm

for one solution. You might try proving it without recourse to sin and cos.