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[IIT 1984] Find the numerical value of tan [ 2*arctan(1/5) - PI/4 ].

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[IIT 1983] Find the value of tan [ arccos(4/5) + arctan(2/3) ].

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[IIT 2001] Find the solutions of arctan{sqrt[x(x+1)]} + arcsin{sqrt[square(x)+x+1]} = PI/2.