Maximum value of $5\sin(200\pi t) + 7\sin(1500\pi t)$ (different frequencies)

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How can I find the maximum value of $5\sin(200\pi t) + 7\sin(1500\pi t)$?

I have tried differentiating to find the maxima, but that is not solvable manually. Is there any common method that can be applied for $n$ terms?