Integral Calculus: JEE Main 2021 Mathematics question

Let T be the tangent to the ellipse E : x² + 4y² = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $\sqrt 5$ is $\alpha$$\sqrt 5$ + $\beta$ + $\gamma$ cos^$-$1$\left( {{1 \over {\sqrt 5 }}} \right)$, then |$\alpha$ + $\beta$ + $\gamma$| is equal to ______________.