Let the line (x-3)/7=(y-2)/-1=(z-3)/-4 intersect the plane containing the lines (x-4)/1=(y+1)/-2=z/1 and 4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a ∈ R at the…

Let the line $\displaystyle \frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}$ intersect the plane containing the lines $\displaystyle \frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1}$ and $\displaystyle 4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a \in \mathbb{R}$ at the point $\displaystyle P(\alpha, \beta, \gamma)$. Then the value of $\displaystyle \alpha+\beta+\gamma$ equals \_\_\_\_.