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[" The base of a triangle is divided into three equal parts.If "t_(1),t_(2),t_(3)" be the tangents of the angles subtended by these "],[" parts at the opposite vertex,prove that: "],[((1)/(t_(1))+(1)/(t_(2)))((1)/(t_(2))+(1)/(t_(3)))=4(1+(1)/(t_(2)^(2)))]

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