Find all Solutions in radians : Sin^2(6x)=1

exact values only

sin(6x)^2 = 1
sin(6x) = -1 , 1
6x = 3pi/2 + 2 * pi * k , pi/2 + 2 * pi * k
6x = (pi/2) * (3 + 4k) , (pi/2) * (1 + 4k)
x = (pi/12) * (3 + 4k) , (pi/12) * (1 + 4k)

From 0 to 2pi

x = pi/12 * (3) , pi/12 * (7) , pi/12 * 11 , pi/12 * 15 , pi/12 * 19 , pi/12 * 23 , pi/12 * 1 , pi/12 * 5 , pi/12 * 9 , pi/12 * 13 , pi/12 * 17 , pi/12 * 21

So:

x = (pi/12) * (1 + 2k)

k is an integer

sin^2(6x) = 1
sin(6x) = 1 or sin(6x) = -1
6x = pi/2 + 2npi or 6x = 3pi/2 + 2npi for all integers, n
x = pi/12 + npi/3 or x = pi/4 + npi/3 for all integers, n

Sin^2u = 1 where sinu= 1 or -1.

This occurs where u = 0 or pi, or k*pi.

u=6x=k*pi

X = (k/6)pi