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arccot( (sqrt(1 + sin x) + sqrt(1 - sin x) ) / (sqrt(1 + sin x) - sqrt(1 - sin x) ) ) = pi/2 - x/2
arccot( (sqrt(1 + sin x) + sqrt(1 - sin x) ) / (sqrt(1 + sin x) - sqrt(1 - sin x) ) ) = pi/2 - x/2
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