prove that $\{a_{n}\} $ converges as $, a_{n+1}=\frac{a_{n}}{sin(a_{n})},\ \forall n\geq2$ and $0<a_{1}<\frac{\pi}{2}$
Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.