Boundary Values & Fourier Series · Medium problem

The Fourier sine series of $f(x) = 1$ on $(0, \pi)$ is $\dfrac4\pi\left(\sin x + \dfrac{\sin 3x}{3} + \dfrac{\sin 5x}{5} + \cdots\right)$. Evaluate it at a suitable point to find $1 - \dfrac13 + \dfrac15 - \dfrac17 + \cdots$.