If $x = f ( y )$ is the solution of the differential equation $\left( 1 + y ^ { 2 } \right) + \left( x - 2 \mathrm { e } ^ { \tan ^ { - 1 } y } \right) \frac { \mathrm { d } y } { \mathrm {~d} x } = 0 , y \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ with $f ( 0 ) = 1$, then $f \left( \frac { 1 } { \sqrt { 3 } } \right)$ is equal to :\\
(1) $e ^ { \pi / 12 }$\\
(2) $e ^ { \pi / 4 }$\\
(3) $e ^ { \pi / 3 }$\\
(4) $e ^ { \pi / 6 }$