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If cot−1(1+sinx+1−sinx1+sinx−1−sinx)=Ax\cot^{-1} \left(\dfrac{\sqrt{1+ \sin x} + \sqrt{1- \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} \right) = Axcot−1(1+sinx−1−sinx1+sinx+1−sinx)=Ax, where 0<x<π20 < x < \dfrac{\pi}{2}0<x<2π, find the value of AAA.
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