At how many points is $f(x) = \lvert \sin x \rvert$ on $(0, 2\pi)$ not differentiable?

Explanation

1. 01

   $\sin x = 0$ inside $(0, 2\pi)$ only at $x = \pi$.

2. 02

   There $\lvert \sin x \rvert$ has a corner: 1 point.