Without using a computer but using pen and paper only, can anyone please help me calculate, simplify / evaluate the following?
$$ \frac{\tan(180^{\circ}/7)}{\tan(360^{\circ}/7)} - \frac{\tan(360^{\circ}/7)}{\tan(540^{\circ}/7)} - \frac{\tan(540^{\circ}/7)}{\tan(180^{\circ}/7)} $$
It evaluates to $-9$. This result is given for reference.