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 \( \triangle ABC \), then \( 15(\alpha + \beta) \) is equal to:
