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I would like to know, if there's a closed form solution to the following problem:

Given a sum of say, 3 sines, with the form y = sin(a.2.PI.t) + sin(b.2.PI.t) + sin(c.2.PI.t) where a,b,c are constants and PI = 3.141592654 and the periods in the expression are multiplication signs, what are the values of t at which two conditions are simultaneously true: (1) y = 0 and (2) the derivative dy/dt > 0. I am calling such points positive zero-crossing points, for want of a better name.

In other words, is there a closed form solution to the two simultaneous conditions:

sin(a.2.PI.t) + sin(b.2.PI.t) + sin(c.2.PI.t) = 0

and

2.PI.a.cos(a.2.PI.t) + 2.PI.b.cos(b.2.PI.t) + 2.PI.c.cos(c.2.PI.t) > 0

Many thanks for any insights and assistance!