Let [·] denote the greatest integer function. If the domain of the function f(x)= sin^-1((x+[x])/3) is [α, β), then α^2+β^2 is equal to:

Let $\displaystyle [\cdot]$ denote the greatest integer function. If the domain of the function $\displaystyle f(x)=\sin ^{-1}\left(\frac{x+[x]}{3}\right)$ is $\displaystyle [\alpha, \beta)$, then $\displaystyle \alpha^2+\beta^2$ is equal to: