I'm trying to show that the Fourier series of $f(\theta) = 0 $ if $|\theta| > \delta$ and $f(\theta) = 1- |\theta|/\delta$ if $|\theta| \leq \delta$
The Fourier coefficients is given by $a_n = 1/2\pi \int_{-\delta}^{\delta} (1- |\theta|/\delta) e^{-in\theta} d\theta$,
where $a_0 = 1/2\pi \int_{-\delta}^{\delta} (1- |\theta|/\delta)d\theta$.
Now $f(\theta) = \delta / 2\pi + 2 \sum_{n=1}^{\infty} (1-cos(n\delta))cos(n\theta)/(n^2\pi\delta)$ I tried to calculate the Fourier coefficients to find the series but I get the wrong result.