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