Let a triangle \( \triangle PQR \) be such that \( P \) and \( Q \) lie on the line \( \frac{x+3}{8} = \frac{y-4}{2} = \frac{x+1}{2} \) and are at a distance of \( 6 \) units from \( R(1, 2, 3) \). If \( (\alpha, \beta, \gamma) \) is the centroid of \( \triangle PQR \), then \( \alpha + \beta + \gamma \) is equal to:
