4cos^2(Pi/8)-4cos^4(Pi/8)-4 = 4*((1+cos(Pi/4))/2) - 4*((1+cos(Pi/4))/2)^2 - 4 = 2*(1+cos(Pi/4)) - (1+cos(Pi/4))^2 - 4 = 2*(1+sqrt(2)/2) - 1 - 2*sqrt(2)/2 - 2/4 - 4 = 2 + 2sqrt(2)/2 - 1 - 2sqrt(2)/2 - 2/4 - 4 = 2 - 1 - 2/4 - 4 = -7/2
Ответ: -7/2