In this paper we review recently established results on the asymptotic behaviour of the trigonometric product $P_n(��) = \prod_{r=1}^n |2\sin ��r ��|$ as $n\to \infty$. We focus on irrationals $��$ whose continued fraction coefficients are bounded. Our main goal is to illustrate that when discussing the regularity of $P_n(��)$, not only the boundedness of the coefficients plays a role; also their size, as well as the structure of the continued fraction expansion of $��$, is important.
To appear in: D. Bilyk, J. Dick, F. Pillichshammer (Eds.) Discrepancy theory, Radon Series on Computational and Applied Mathematics