Let $(a,b)\subset(0,2\pi)$ be the largest interval for which $\sin^{-1}(\sin\theta)-\cos^{-1}(\sin\theta)>0,\ \theta\in(0,2\pi)$, holds. If $\alpha x^{2}+\beta x+\sin^{-1}(x^{2}-6x+10)+\cos^{-1}(x^{2}-6x+10)=0$ and $\alpha-\beta=b-a$, then $\alpha$ is equal to: