Given, sin 4x + sin 2x = 0

=> sin (2*2x) + sin 2x = 0

=> 2*sin 2x * cos 2x + sin 2x = 0

=> (sin 2x)[1 + 2cos 2x] = 0

=> sin 2x = 0

or 1 + 2cos 2x = 0

=> 2cos 2x = -1

=> cos 2x = -1/2

when sin 2x = 0

     2x = 0, π, 2π, 3π

=> x = 0, π/2, π, π/2

when cos 2x = -1/2

     2x = 2π/3, 4π/3, 8π/3, 10π/3

=> x = π/3, 2π/3, 4π/3, 5π/3

So, x = 0, π/2, π, 3π/2 , π/3, 2π/3, 4π/3, 5π/3