Ctg (7arcctg-√3+25π/4)

Ctg (7arcctg (-√3) + 25π/4) = Ctg (7 (5π/6) + 6π+π/4) = Ctg (35π/6+π/4) =

=Ctg (6π-π/6+π/4) = Ctg (-2π/12+3π/12) = Ctg (π/12) = cos (π/12) / sin (π/12) =

=2cos² (π/12) / [2cos (π/12) sin (π/12) ] = (1+cos (π/6)) / (sin (π/6) =

= (1+√3/2) / (1/2) = 2+√3