Consider the function f : (−π/2, π/2) → (−∞, ∞) 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 α be the total number of points in the interval (−π/2, π/2) at which f is NOT continuous, and let β be the total number of points in the interval (−π/2, π/2) at which f is NOT differentiable. Then the value of α + β is ___________.