Let $y = y(x)$ be the solution of the differential equation $\frac { d y } { d x } = \frac { \tan x + y } { \sin x \sec x - \sin x \tan x } , \quad x \in \left(0, \frac { \pi } { 2 }\right)$ satisfying the condition $y\left(\frac { \pi } { 4 }\right) = 2$. Then, $y\left(\frac { \pi } { 3 }\right)$ is\\
(1) $\sqrt { 32 } + \log _ { e } \sqrt { 3 }$\\
(2) $\frac { \sqrt { 3 } } { 2} \left(2 + \log _ { e } 3\right)$\\
(3) $\sqrt { 3 } \left(1 + 2 \log _ { e } 3\right)$\\
(4) $\sqrt { 3 } \left(2 + \log _ { e } 3\right)$