Finding PDF of max of sum of truncated sinusoids

Suppose I am adding N sinusoids. The frequencies, phases, and amplitudes are chosen to be iid in the range f1 to f2, 0 to 2pi, and A1 to A2 respectively. Now, if I am observing the sum from time t1 to t2, how do I approach finding a pdf associated with the maximum of the sum? Specifically, I am trying to find a mathematical expression for the pdf of the maximum as a function of N, f1, f2, A1, A2, and (t2-t1). Thank you for your time.