Для вычисления данного выражения воспользуемся формулами:
sin(3θ) = 3sinθ - 4sin³θ
cos(3θ) = 4cos³θ - 3cosθ

У нас дано выражение: sin(π/8) cos³(π/8) sin³(π/8)

sin(π/8) cos³(π/8) sin³(π/8) = sin(π/8) (4cos³(π/8) - 3cos(π/8)) (3sin(π/8) - 4sin³(π/8))
= sin(π/8) (4cos³(π/8) - 3cos(π/8)) (3sin(π/8) - 4sin(3π/8))
= sin(π/8) (4cos³(π/8) - 3cos(π/8)) (3sin(π/8) - 4(3sin(π/8) - 4sin(π/8)))
= sin(π/8) (4cos³(π/8) - 3cos(π/8)) (3sin(π/8) - 12sin(π/8) + 16sin(π/8))
= sin(π/8) (4cos³(π/8) - 3cos(π/8)) (4sin(π/8))
= sin(π/8) (4cos(3π/8)) (4sin(π/8))
= sin(π/8)sin(3π/8)
= sin(π/8)sin(π-2π/8)
= sin(π/8)*sin(π/4)

Таким образом, sin(π/8)cos³(π/8)sin³(π/8) = sin(π/8)sin(π/4) = sin(π/8)√2/2 = √2/4.