# Inspired by Aakash Khandelwal

Geometry Level 5

If $$a_0=\sin^2\left (\dfrac{\pi}{45} \right)$$ and $$a_{n+1}=4a_{n}(1-a_{n})$$ for $$n\geq 0$$, find the smallest positive integer $$n$$ such that $$a_n=a_0$$.

If you come to the conclusion that no such $$n$$ exists, enter 666.

×