I'm very rusty on this, but assume we have a function such that the Fourier sine series for f is

Then we need to invert the Fourier sine series, which if I remember correctly means that

Someone needs to check me on that result, but it's going to be something of the sort. (The best way for you, kamaksh_ice, to check me is to do the problem then take the Fourier sine series of the result and see if you get your original series back.)

-Dan