Area Under The Curves

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 ______________.