If y=y(x) is the solution of the equation e^sin y cos y (d y)/(d x)+ e^sin y cos x= cos x, y(0)=0; then 1+y((π)/6)+(√ 3)/2 y((π)/3)+1/(√ 2) y((π)/4)…

If $\displaystyle y=y(x)$ is the solution of the equation $\displaystyle \mathrm{e}^{\sin y} \cos y \frac{\mathrm{~d} y}{\mathrm{~d} x}+\mathrm{e}^{\sin y} \cos x=\cos x, y(0)=0$; then $\displaystyle 1+y\left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2} y\left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}} y\left(\frac{\pi}{4}\right)$ is equal to \_\_\_\_.