Question 14
On two parallel lines, the distinct points $A_{1}, A_{2}, A_{3}, \ldots$ respectively $B_{1}$, $B_{2}, B_{3}, \ldots$ are marked in such a way that $|A_{i}A_{i+1}|=1$ and $|B_{i}B_{i+1}|=2$ for $i=1,2, \ldots$ (see Figure). Provided that $\angle A_{1}A_{2}B_{1}=\alpha$, find the infinite sum $\angle A_{1}B_{1}A_{2}+\angle A_{2}B_{2}A_{3}+\angle A_{3}B_{3}A_{4}+\ldots$
