# Zeros of random trigonometric polynomials

For a certain nonconvex optimization problem, I need to know the expected number of real zeros of trigonometric polynomials.

$0=\sum_{k=1}^{k=N}A(k)\sin(kx)A(k)\cos(kx)$

This is not exactly the usual sense of polynomial.

This is well studied for i.i.d. standard normal coefficients $$A(k),b(k)$$. I need more general results; in particular I need to relax the identical distribution assumption. I wonder if this is a case where a worst-case result might be easier than a stochastic one?