Solving an inequality of the form $a\cos(nt) + b\cos(mt) + \cdots > k$

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I need to find where sums of a different scaling and frequencies of a given periodic function become greater than a constant. For this example I chose cosine, but if there is a way to solve it for example for square waves, etc please let me know.

$n,~ m,~ \cdots~$ are integers $~a,~b,~\cdots~$ are real and $~k~$ is a real constant. I need to solve it for $~t~$. The number of terms on the left is finite.

The inequality:

$$a\,\cos(nt)+b\,\cos(mt) + c\,\cos(lt) + \cdots >k$$

If not in the continuous domain, can it be analytically solved in the discrete domain?