The base of a triangle is divided into three equal parts. If `t_1, t_2,t_3` are 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))dot`

Answer

`4(1+(1)/(t_(2)^(2)))=((1)/(t _(1))+ (1)/(t_(1)))((1)/(t_(2))+(1)/(t_(2)))`