Cos0+cospi/7+cos2pi/7+cos3pi/7+cos4pi/7+cos5pi/7+cos6pi/7

cos0 + [cos(6π/7)+cos(π/7)] + [cos(5π/7)+cos(2π/7)] + [cos(4π/7)+cos(3π/7)] =

1 +2cos(π/2)cos(5π/7) + 2cos(π/2)cos(3π/2) + 2cos(π/2)cos(π/2) = 1      

cos0=1,

cospi/7+cos2pi/7+cos3pi/7+cos4pi/7+cos5pi/7+cos6pi/7=cos21pi/7=cos3pi=cos(2pi+pi)=cospi=-1,

Теперь подставляем,получается

1-1=0