Value of tan^-12+tan^-13+tan^-14 is equal to :

$\tan^{-1}2+\tan^{-1}3+\tan^{-1}4$

$=π+\tan^{-1}\left(\frac{2+3}{1-2×3}\right)+\tan^{-1}4$ (π add as 1-2.3<0)

so $π-\tan^{-1}1+\tan^{-1}4$

$=π+\tan^{-1}\left(\frac{4-1}{1+4.1}\right)$

$=π+\tan^{-1}\left(\frac{3}{5}\right)$