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