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Find arctan r + arctan s +arctan t

Source: IberoAmerican 1987 Q5

November 12, 2010
algebra unsolvedalgebra

Problem Statement

Let r,s,tr,s,t be the roots of the equation x(x−2)(3x−7)=2x(x-2)(3x-7)=2. Show that r,s,tr,s,t are real and positive and determine arctan⁡r+arctan⁡s+arctan⁡t\arctan r+\arctan s +\arctan t.
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