Let the line l: x=(1-y)/-2=(z-3)/(λ), λ ∈ R meet the plane P: x+2 y+3 z=4 at the point (α, β, γ). If the angle between the line l and the plane P is…

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