Trigonometry

Key theorem: sin2A = 2sinAcosA

sin(π/5)cos(π/5)cos(2π/5)cos(4π/5)cos(18π/5)

= sin(π/5)cos(π/5)cos(2π/5)cos(4π/5)cos(8π/5)

= (1/2)(2)sin(π/5)cos(π/5)cos(2π/5)cos(4π/5)cos(8π/5)

= (1/2)sin(2π/5)cos(2π/5)cos(4π/5)cos(8π/5)

= (1/4)sin(4π/5)cos(4π/5)cos(8π/5)

= (1/8)sin(8π/5)cos(8π/5)

= (1/16)sin(16π/5)

= -(1/16)sin(π/5)

So, cos(π/5)cos(2π/5)cos(4π/5)cos(18π/5) = -1/16