Prove: cos(π/5) × cos(2π/5) × cos(4π/5) × cos(8π/5) = −1/16

LHS = cos(π/5) × cos(2π/5) × cos(4π/5) × cos(8π/5)

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

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

= (1 / (8 sin(π/5))) · sin(8π/5) · cos(8π/5)

= sin(16π/5) / (16 sin(π/5)) = sin(3π + π/5) / (16 sin(π/5))

= (−sin(π/5)) / (16 sin(π/5))

= −1/16