How can I solve for $t$ given,
$$ 0 = \frac{2\Pi}{T} \sum_{k=1}^N k(a_k cos(2\Pi\frac{k}{T}t) - b_k sin(2\Pi\frac{k}{T}t)) $$
What I am trying to do is, given a complex wave in the form of a Fourier Series, taking the first order derivative to find all the crests and troughs of the wave within one time period $T$.