Let $-\frac{\pi}{6}<\theta<-\frac{\pi}{12}$. Suppose $\alpha_{1}$ and $\beta_{1}$ are the roots of the equation $x^{2}-2 x \sec \theta+1=0$ and $\alpha_{2}$ and $\beta_{2}$ are the roots of the equation $x^{2}+2 x \tan \theta-1=0$. If $\alpha_{1}>\beta_{1}$ and $\alpha_{2}>\beta_{2}$, then $\alpha_{1}+\beta_{2}$ equals