Fourier Series of Sin^2(x)

Hello. We were asked to perform the Fourier Series of Sin\(^{2}\)(x). I just want to ask if I did it the right way.

I stopped right after I got the A\(_{k}\) since I'm not sure if I'm doing it correctly. Also, I plotted the above equation in MATLAB and found out that it is an even function so I suppose B\(_{k}\) = 0.

Below is my solution. Sorry for my bad handwriting.