Question 42
Verify the correctness of the equality
$$
\tan \alpha + 2 \tan 2\alpha + 2^2 \tan 2^2 \alpha + \dots + 2^n \tan 2^n \alpha = \cot \alpha - 2^{n+1} \cot 2^{n+1} \alpha.
$$
$$
\tan \alpha + 2 \tan 2\alpha + 2^2 \tan 2^2 \alpha + \dots + 2^n \tan 2^n \alpha = \cot \alpha - 2^{n+1} \cot 2^{n+1} \alpha.
$$