Let \( a, b, c \) be in arithmetic progression. Let the centroid of the triangle with vertices \( (a, c) \), \( (2, b) \) and \( (a, b) \) be \( \left( \frac{10}{3}, \frac{7}{3} \right) \). If \( \alpha, \beta \) are the roots of the equation \( a x^2 + b x + 1 = 0 \), then the value of \( \alpha^2 + \beta^2 - \alpha \beta \) is:
