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Hi everyone, I've been looking for the finite sum formulae of trig functions. I've found the easiest ones (sine and cosine). But the one for the tangent seems to be very hard. No mathematical tricks work. Plus I've looked it up on the internet. Nothing. I will greatly appreciate your help. Thanks in advance.

tan x + tan (2x) + tan (3x) + ... + tan (nx) = ???

tan x + tan (2x) + tan (3x) + ... + tan (nx) = ???

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