Limit of a Definite Integral 3

$\large \lim_{n\to\infty} \int_0^{n\pi} e^{-x} |\sin(x)| \, dx$

If the limit above can be expressed as $\alpha \left( \frac{1+e^\beta}{1-e^\lambda} \right)$ where $\alpha, \beta, \lambda$ are real numbers, $\alpha \geq 0$ and $\beta, \lambda \leq 0$ and $n$ is an integer, find the value of $2(\alpha+\beta-\lambda)$ .