Find the value of

(1 + cos(π/8))(1 + cos(3π/8))(1 + cos(5π/8))(1 + cos(7π/8))

(1 + cos(π/8))(1 + cos(3π/8))(1 + cos(5π/8))(1 + cos(7π/8))

= (1 + cos(π/8))(1 + cos(3π/8))(1 + cos(π − 3π/8))(1 + cos(π − π/8))

= (1 − cos²(π/8))(1 − cos²(3π/8))

= sin²(π/8) × sin²(3π/8)

= (1/4)(1 − cos(π/4))(1 − cos(3π/4))

= (1/4)(1 − cos(π/4))(1 + cos(π/4))

= (1/4)(1 − cos²(π/4))

= (1/4)(1 − 1/2)

= 1/8