Help with Infinite Series: sum[1,infty] sin(nx)/(n^2) w/ period of 0 to 2π

[ethacetin]

Hello,

I was wondering if anyone could help me with this problem, but I can't even remember how to set up these types of questions.

I want to calculate the summation from 1 to infinity of sin(nx)/(n^2) with a period of 0 to 2π.

In other words, sin(x) + sin(2x)/(2^2) + sin(3x)/(3^2) + ...

I know that it converges on a sinusoidal function with the same period as sin(x). I even know what the shape of that curve looks like from manually adding enough of the series together, but I would really like to know the exact equation of the sinusoidal function being produced.

 

[ethacetin]

Sorry if this looks like I'm asking for help with a homework problem. This is just for a hobby. I haven't been in school for almost a decade now. I aced my calculus classes back then, and even used to tutor a bit myself, but I've forgetting a lot of the material.
It's not even so much this exact problem either. I would like to know in general how to solve these types of problems. If anyone could provide links to sample problems involving infinite series of sinusoidal waves or even point me in the right direction that would be really helpful.