sin^2 x+sin^2 2x=sin^2 2x+sin^2 4x
<=> sin^2 x=sin^2 4x
<=> sin4x = sinx (1) hoặc sin4x = -sinx(2)
(1)<=>4x=x+k2π hoặc 4x=π-x+k2π
<=>3x=k2π hoặc 5x=π+k2π
<=>x=k2π/3 hoặc x=π/5+k2π/5 (k∈Z)
(2)<=>sin4x=sin(-x)
<=>4x=-x+k2π hoặc 4x=π-(-x)+k2π
<=>5x=k2π hoặc 3x=π+k2π
<=>x=k2π/5 hoặc x=π/3+k2π/3 (k∈Z)
Vậy S={k2π/3;π/5+k2π/5;k2π/5;π/3+k2π/3|k∈Z}