Consider the function \( f : \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \rightarrow (-\infty, \infty) \) defined by
\( f(x) = (|x| + |x - 1|)\sin x + [ x\sin x ]\), where \( [x\sin x ]\) 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 __________.
