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:
(1) $- \frac { 71 } { 256 }$
(2) $\frac { 69 } { 256 }$
(3) $\frac { 71 } { 256 }$
(4) $- \frac { 69 } { 256 }$