If the solution $y ( x )$ of the given differential equation $\left( \mathrm { e } ^ { y } + 1 \right) \cos x \mathrm {~d} x + \mathrm { e } ^ { y } \sin x \mathrm {~d} y = 0$ passes through the point $\left( \frac { \pi } { 2 } , 0 \right)$, then the value of $\mathrm { e } ^ { y \left( \frac { \pi } { 6 } \right) }$ is equal to $\_\_\_\_$