Let two vertices of a triangle \( ABC \) be \( (2, 4, 6) \) and \( (0, -2, -5) \), and its centroid be \( (2, 1, -1) \). If the image of the third vertex in the plane \( x + 2y + 4z = 11 \) is \( (\alpha, \beta, \gamma) \), then \( \alpha\beta + \beta\gamma + \gamma\alpha \) is equal to:
