Three Dimensional Geometry: JEE Main 2023 Mathematics question

Let $\mathrm{P}_{1}$ be the plane $3 x-y-7 z=11$ and $\mathrm{P}_{2}$ be the plane passing through the points $(2,-1,0),(2,0,-1)$, and $(5,1,1)$. If the foot of the perpendicular drawn from the point $(7,4,-1)$ on the line of intersection of the planes $P_{1}$ and $P_{2}$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to ___________.