In an isosceles triangle $ABC$, the vertex $A$ is $( 6,1 )$ and the equation of the base $BC$ is $2x + y = 4$. Let the point $B$ lie on the line $x + 3y = 7$. If $( \alpha , \beta )$ is the centroid of the triangle $ABC$, then $15( \alpha + \beta )$ is equal to