If the domain of the function $f(x) = {\log _e}\left( {\frac{{2x - 3}}{{5 + 4x}}} \right) + {\sin ^{ - 1}}\left( {\frac{{4 + 3x}}{{2 - x}}} \right)$ is $[\alpha ,\beta )$ , then ${\alpha ^2} + 4\beta $ is equal to
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