If the domain of the function $f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{{2x - 1} \over 2}} \right)} }}$ is the interval ($\alpha$, $\beta$], then $\alpha$ + $\beta$ is equal to :