If the solution curve y=y(x) of the differential equation $\left(1+y^2\right)\left(1+\log _e x\right) d x+x d y=0, x>0$ passes through the point (1,1) and $y(e)=\frac{\alpha-\tan \left(\frac{3}{2}\right)}{\beta+\tan \left(\frac{3}{2}\right)}$, then $\alpha+2 \beta$ is
