Question 20
Let $D$ be a point on the side $\overline{BC}$ of triangle $ABC$. Denote $\alpha_1 = \angle DAB$ and $\alpha_2 = \angle CAD$. Prove the equality
$$
\frac{\sin(\alpha_1 + \alpha_2)}{|AD|} = \frac{\sin \alpha_1}{|AC|} + \frac{\sin \alpha_2}{|AB|}.
$$
$$
\frac{\sin(\alpha_1 + \alpha_2)}{|AD|} = \frac{\sin \alpha_1}{|AC|} + \frac{\sin \alpha_2}{|AB|}.
$$