Let $y = y ( x )$ be the solution of the differential equation $\cos x ( 3 \sin x + \cos x + 3 ) d y = ( 1 + y \sin x ( 3 \sin x + \cos x + 3 ) ) d x , 0 \leq x \leq \frac { \pi } { 2 } , y ( 0 ) = 0$. Then, $y \left( \frac { \pi } { 3 } \right)$ is equal to:\\
(1) $2 \log _ { \mathrm { e } } \left( \frac { 2 \sqrt { 3 } + 9 } { 6 } \right)$\\
(2) $2 \log _ { \mathrm { e } } \left( \frac { 2 \sqrt { 3 } + 10 } { 11 } \right)$\\
(3) $2 \log _ { \mathrm { e } } \left( \frac { \sqrt { 3 } + 7 } { 2 } \right)$\\
(4) $2 \log _ { \mathrm { e } } \left( \frac { 3 \sqrt { 3 } - 8 } { 4 } \right)$