记18°=t
则5t=90°
sin3t=cos2t
sin(t+2t)=cos2t
sintcos2t+costsin2t=cos2t
sint(1-2sin²t)+2sint(1-sin²t)=1-2sin²t
记sint=x,则
x(1-2x²)+2x(1-x²)=1-2x²
(x-1)(4x²+2x-1)=0
x≠1,所以4x²+2x-1=0,取正根得：
x=(√5-1)/4即为sin18°的值.