Let $z$ be a complex number such that $| z + 2 | = 1$ and $\operatorname { Im } \left( \frac { z + 1 } { z + 2 } \right) = \frac { 1 } { 5 }$. Then the value of $| \operatorname { Re } ( \overline { z + 2 } ) |$ is\\
(1) $\frac { 2 \sqrt { 6 } } { 5 }$\\
(2) $\frac { 24 } { 5 }$\\
(3) $\frac { 1 + \sqrt { 6 } } { 5 }$\\
(4) $\frac { \sqrt { 6 } } { 5 }$