Could I get anymore Tanner?

Geometry Level 3

tan(α)+2tan(2α)+4tan(4α)+8cot(8α)=cot(nα)\tan(\alpha)+2\tan(2\alpha)+4\tan(4\alpha)+8\cot(8\alpha)=\cot(n\alpha)

If the above trigonomtric equation is true for all α\alpha, what is the value of nn?

This problem is part of the set Trigonometry.

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