Find the solutions of the equation that are in the interval

Find the solutions of the equation that are in the interval [0, 2).

cos u cos 2u = 0

in the interval [0, 2).

cos u cos 2u = 0

use the formula : cosx - cosy =-2sin(x+y)/2*sin(x-y)/2

sin(3u/2)*sin(u/2) =0

sin(3u/2) =0

3u/2 = 0 +2pi*n

u = 4pi*n/3

3u/2 = pi +2pi*n ---> u = (2pi + 4pi*n)/3

n=0 ; u =0,

n=1 , u = 2pi/3

u = (2pi + 4pi*n)/3

n=0 ; u = 4pi/3

sin(u/2) =0

u = 4pi*n ; u = 2pi +4pi*n

Only ; n=0 ; u =0 is the solution in the interval [0, 2)

Solution : u =0, 2pi/3, 4pi/3