I'm having a doubt on solving the below question.

Question

Question: drive google(dot)com/file/d/1OOL_WecZgLk3fcd65UxVzec4T9Y7ztuB/view?usp=sharing

Apparently we can write t as, t = (4/pi)* ( (-1)^(n+1) ) * [sigma n=1-infinity { (sin((n*pi*t)/2) } ]

Hw can I find the Fourier series of f(t) = t^2?

Can I take bn = (4/pi)*((-1)^(n+1)) and use Parsvel's identity to find the Fourier series of f(t) = t^2, which is the square of t?

Or else, if we're to use the property that t^2 = integration of 0.5*t, how can we do it?

What's the most ideal way to solve this problem?

Thank you in advance for your help!