For positive integers $n \geq 2$, let $a_n = \lceil n/\pi \rceil$ and let $b_n = \lceil \csc (\pi/n) \rceil$. Is $a_n = b_n$ for all $n \neq 3$?

Solutions are due May 13th (Friday), 6PM, and it will remain open if nobody solved it.