If \(a_0 = \sin^2 \left( \frac{\pi}{45} \right)\) and \(a_{n + 1} = 4a_n (1 - a_n)\) for \(n \ge 0,\) find the smallest positive integer \(n\) such that \(a_n = a_0.\)
Using my calculator, I got a9 = a0.
+159 
