In the integral \( \displaystyle \int_{0}^{10} \frac{[\sin 2\pi x]}{e^{\,x-[ x ]}} \, dx = \alpha e^{-1} + \beta e^{-1/2} + \gamma \), where \( \alpha, \beta, \gamma \) are integer and \( [x] \) denotes the greatest integer less than or equal to \( x \), then the value of \( \alpha + \beta + \gamma \) is equal to:
