Question: Bessel simplification?

Hi there, I'm trying to express the following expression

sin(c + I * (sin (d + k * sin(t)))


in terms of Bessel functions. I've been knocking my head against it trying to do it by hand for a while now and someone suggested maple could help.

So far I've just written out the equation, and expanded it giving a 3 line long trignometric equation. I'm hoping now to simplify it in terms of sums of Bessel functions. Will maple be able to help me out with that?

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