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.