If for the solution curve $y = f ( x )$ of the differential equation $\frac { \mathrm { d } y } { \mathrm {~d} x } + ( \tan x ) y = \frac { 2 + \sec x } { ( 1 + 2 \sec x ) ^ { 2 } }$, $x \in \left( \frac { - \pi } { 2 } , \frac { \pi } { 2 } \right) , f \left( \frac { \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 10 }$, then $f \left( \frac { \pi } { 4 } \right)$ is equal to :\\
(1) $\frac { \sqrt { 3 } + 1 } { 10 ( 4 + \sqrt { 3 } ) }$\\
(2) $\frac { 5 - \sqrt { 3 } } { 2 \sqrt { 2 } }$\\
(3) $\frac { 9 \sqrt { 3 } + 3 } { 10 ( 4 + \sqrt { 3 } ) }$\\
(4) $\frac { 4 - \sqrt { 2 } } { 14 }$