Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y'' + y' \sin(x) + y \sin(2x) = 0$ with boundary conditions $y(0) = \pi, y(\pi) = 0$ in the limit $\epsilon \to 0^+$. Use only the variables and constants given in the problem; do not define additional constants. Place your final solution in a $\boxed{}$ LaTeX environment.
Solution: $\boxed{\pi - \sqrt{2\pi} \int_0^{\frac{x}{\sqrt{\epsilon}}} e^{-s^2/2} \, ds}$