The original question from the Shanxi Mobile Online Business Hall is as follows: Let the function $ f(x) $ be continuous on $[0, \pi]$, and the integral of $ f(x) $ over the interval $[0, \pi]$ is 0. Also, the integral of $ f(x)\cos x $ over the interval $[0, \pi]$ is 0. Prove that there exist at least two distinct points $ x_1 $ and $ x_2 $ in $(0, \pi)$ such that $ f(x_1) = f(x_2) = 0 $.