Question 76
Let $n$ be a positive integer and $a_0, a_1, \dots, a_{2n} \in \left\langle -\frac{\pi}{2}, \frac{\pi}{2} \right\rangle$ real numbers such that
$$
\tan a_k = 2^{k-n} \quad \text{for} \quad k = 0, 1, \dots, 2n.
$$
Determine the sum $a_0 + a_1 + \dots + a_{2n}$.
$$
\tan a_k = 2^{k-n} \quad \text{for} \quad k = 0, 1, \dots, 2n.
$$
Determine the sum $a_0 + a_1 + \dots + a_{2n}$.