3d Geometry

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 ___________.