Limits Continuity And Differentiability

Consider the function $f:\left(-\frac{\pi}{2},\frac{\pi}{2}\right) \to (-\infty, \infty)$ defined by

\(f(x) = (|x| + |x-1|) \sin x + \left[ x \sin x \right],\)

where $\left[ x \sin x \right]$ is the greatest integer less than or equal to $x \sin x$.

Let $\alpha$ be the total number of points in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ at which $f$ is NOT continuous, and let $\beta$ be the total number of points in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ at which $f$ is NOT differentiable.

Then the value of $\alpha + \beta$ is ____________.