For a positive real number $t$, let $f ( t )$ be the value of the real number $a$ such that the curve $y = t ^ { 3 } \ln ( x - t )$ meets the curve $y = 2 e ^ { x - a }$ at exactly one point. Find the value of $\left\{ f ^ { \prime } \left( \frac { 1 } { 3 } \right) \right\} ^ { 2 }$. [4 points]