Evaluation of a trigonometric series $$
\mbox{Question: Evaluate}\quad
\tan^{2}\left(\pi \over 16\right) + \tan^{2}\left(2\pi \over 16\right) + \tan^{2}\left(3\pi \over 16\right) + \cdots + \tan^{2}\left(7\pi \over 16\right)
$$
What I did:
Well I know that $\tan^{2}\left(7\pi/16\right)$ is the same as
$\cot^{2}\left(\pi/16\right)$. Thus this will repeat for all values up to
$\tan^{2}\left(4\pi/16\right)$.
However, I don't understand where to proceed from there. 

HINT: Use the half angle formula with $\theta = \pi/4$ to find $\tan(\pi/8)$ and do the same with $\theta = \pi/8$ to find $\tan(\pi/16)$
EDIT: The half angle formula is:
$$\tan(a) = \frac{2\tan(\frac{a}{2})}{1- \tan^2(\frac{a}{2})}$$
So use this formula for $a = \pi/4$ and $a = \pi/8$
