What are the solutions of the equation 2sin(4x)=1 on the interval [0,π)?

2sin (4x)  =  1                 divide both sides  by 2

sin (4x)  =  1/2

Note  that  sin  (x)  = 1/2  at     pi/6, 5pi/6, 13pi/6, 17pi/6

Dividing  these angles  by 4    gives  us  the solutions

x  =  pi/24 , 5pi/24, 13 pi/24 , 17 pi /24