$\sin x+\dfrac{\sin 2x}{2}+\dfrac{\sin 3x}{3}+\cdots$ is positive

$\sin x+\dfrac{\sin 2x}{2}+\dfrac{\sin 3x}{3}+\cdots$ is positive

Let $0<x<\pi$. $n$ be a natural number.
How to prove
$$\sin x+\dfrac{\sin 2x}{2}+\dfrac{\sin 3x}{3}+\ldots+ \dfrac{\sin nx}{n}>0$$