so here is my problem

tan theta + tan(theta +120degrees) + tan(theta + 240 degrees) = 3tan(3theta)

and here is what the answer is supposed to be......

tan + cot(pi/6-theta) - cot(theta + pi/6) = 3tan(3theta)

i get pretty far in my simplification process, what I don't understand is how does 120 degrees and 240 degrees each become pi/6? This is probably something really simple but if someone could please take pity on me and explain it, I would be most grateful!

sincerely

Nikki