Can anyone help me find a formal reference for the following identity about the summation of squared tangent function:
$$ \sum_{k=1}^m\tan^2\frac{k\pi}{2m+1} = 2m^2+m,\quad m\in\mathbb{N}^+. $$
I have proved it, however, the proof is too long to be included in a paper. So I just want to refer to some books or published articles.
I also found it to be a special case of the following identity,
$$ \sum_{k=1}^{\lfloor\frac{n-1}{2}\rfloor}\tan^2\frac{k\pi}{n} = \frac16(n-1)(-(-1)^n (n + 1) + 2 n - 1),\quad n\in\mathbb{N}^+ $$
which is provided by Wolfram.
Thank you very much!
