Put 6x = u. Now, for u in [0,2pi), tan(u) = 1, ie., u = (1 or 5)(pi/4) rad & x = u/6 = (1 or 5)(pi/24) rad.

6x = π/4 + kπ

x = π/24 + kπ/6

π/24 + 4kπ/24 < 2π

1/24 + 4k/24 < 2

1 + 4k < 48

0 ≤ k ≤ 11

1) Your solution is a little wrong. It should be (pi/24) + (pi/6) * k

2) Set your solution to the domain and solve for k

0 < pi/24 + (pi/6) * k < 2pi

-pi/24 < (pi/6) * k < 47pi/24

(-pi/24) * (6/pi) < k < (47pi/24) * (6/pi)

-1/4 < k < 47/4

k = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11

pi/24

5pi/24

9pi/24

13pi/24

17pi/24

21pi/24

25pi/24

29pi/24

33pi/24

37pi/24

41pi/24

45pi/24