How to show that $\tan(n), n\in \mathbb{N}$ is not bounded I'm struggling on how to show that the sequence of $\tan(n)$ is not bounded. Can you please give me some help?

Hint. Prove that $\forall \varepsilon > 0$ there are infinitely many $n \in \mathbb{N}$ such that 
$$
n\ (\text{mod }2\pi) \in \left(\frac{\pi}{2}-\varepsilon, \frac{\pi}{2}+\varepsilon\right).
$$
The simplest way to do this is to use Dirichlet's principle.
