  Let $X_N$ be a random trigonometric polynomial of degree $N$ with iid
coefficients and let $Z_N(I)$ denote the (random) number of its zeros lying in
the compact interval $I\subset\mathbb{R}$. Recently, a number of important
advances were made in the understanding of the asymptotic behaviour of $Z_N(I)$
as $N\to\infty$, in the case of standard Gaussian coefficients. The main
theorem of the present paper is a universality result, that states that the
limit of $Z_N(I)$ does not really depend on the exact distribution of the
coefficients of $X_N$. More precisely, assuming that these latter are iid with
mean zero and unit variance and have a density satisfying certain conditions,
we show that $Z_N(I)$ converges in distribution toward $Z(I)$, the number of
zeros within $I$ of the centered stationary Gaussian process admitting the
cardinal sine for covariance function.
