  In this paper we review recently established results on the asymptotic
behaviour of the trigonometric product $P_n(\alpha) = \prod_{r=1}^n |2\sin \pi
r \alpha|$ as $n\to \infty$. We focus on irrationals $\alpha$ whose continued
fraction coefficients are bounded. Our main goal is to illustrate that when
discussing the regularity of $P_n(\alpha)$, not only the boundedness of the
coefficients plays a role; also their size, as well as the structure of the
continued fraction expansion of $\alpha$, is important.
