Instead, consider that $ f(\theta) = \sin(3\theta) + \cos(4\theta) $ is differentiable, and $ f'(\theta) = 3\cos(3\theta) - 4\sin(4\theta) $. The number of solutions to $ |f(\theta)| = 1 $ is discrete and finite in any bounded interval if we consider level sets — but actually, it's continuous, so it crosses $ \pm1 $ infinitely often? Wait: $ \theta \in [0,7\pi) $ is infinite, but the problem likely assumes one full cycle of the group behavior — but no time bound was given. - Portal da Acústica