6. (10%) The function $f(x)$ be partially defined by $$f(x) = \begin{cases} \frac{\pi}{2}, & 0 < x \le \frac{\pi}{2}, \\ \pi - x, & \frac{\pi}{2} < x < \pi. \end{cases}$$ If $f(x)$ is an odd periodic function with period $2\pi$, find its Fourier series representation.