  We prove a Central Limit Theorem for the number of zeros of random
trigonometric polynomials of the form $K^{-1/2}\sum_{n=1}^{K} a_n\cos(nt)$,
being $(a_n)_n$ independent standard Gaussian random variables. In particular,
we prove the conjecture by Farahmand, Granville & Wigman that the variance is
equivalent to $V^2K$, $0<V^2<\infty$, as $K\to\infty$. % The case of stationary
trigonometric polynomials was studied by Granville & Wigman and by Aza\"\is &
Le\'on. Our approach is based on the Hermite/Wiener-Chaos decomposition for
square-integrable functionals of a Gaussian process and on Rice Formula for
zero counting.
