  In this paper, we quantify the rate of convergence between the distribution
of number of zeros of random trigonometric polynomials (RTP) with i.i.d.
centered random coefficients and the number of zeros of a stationary centered
Gaussian process G, whose covariance function is given by the sinc function.
First, we find the convergence of the RTP towards G in the Wasserstein-1
distance, which in turn is a consequence of Donsker Theorem. Then, we use this
result to derive the rate of convergence between their respective number of
zeros. Since the number of real zeros of the RTP is not a continuous function,
we use the Kac-Rice formula to express it as the limit of an integral and, in
this way, we approximate it by locally Lipschitz continuous functions.
