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- #1

$$

a_0 = \frac{1}{\pi}\int_{-\pi}^{\pi}\theta^2 d\theta = \frac{2\pi^2}{3}

$$

$$

a_n = \frac{1}{\pi}\left[\left.\frac{\theta^2}{n}\sin n\theta\right|_{-\pi}^{\pi}-\frac{1}{n}\left[\left.\frac{-\theta}{n}\cos n\theta\right|_{-\pi}^{\pi}+\int_{-\pi}^{\pi}\cos n\theta d\theta\right]\right] = \frac{2}{n\pi}\left[\pi^2\sin n\pi - \frac{1}{n}\sin n\pi\right]

$$

However, since I have only sine, all the coefficients would be zero. Is that correct?