  We compute the variance asymptotics for the number of real zeros of
trigonometric polynomials with random dependent Gaussian coefficients and show
that under mild conditions, the asymptotic behavior is the same as in the
independent framework. In fact our proof goes beyond this framework and makes
explicit the variance asymptotics of various models of random Gaussian
polynomials. Though we use the Kac--Rice formula, we do not use the explicit
closed formula for the second moment of the number of zeros, but we rather rely
on intrinsic properties of the Kac--Rice density.
