Inverse Trigonometric Functions

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 :