Let the line $$L: x = \frac{1-y}{-2} = \frac{z-3}{\lambda}$$, $$\lambda \in \mathbb{R}$$ meet the plane $$P: x + 2y + 3z = 4$$ at the point $$(\alpha, \beta, \gamma)$$. If the angle between the line $$L$$ and the plane $$P$$ is $$\cos^{-1}\left(\sqrt{\frac{5}{14}}\right)$$, then $$\alpha + 2\beta + 6\gamma$$ is equal to _______