Trigonemetric Functions - Need help understanding constraints

Hello,

Can someone please help me understand how the answers were obtained?

1. (sqrt3)tanx+1=0 -----> tanx = -1/(sqrt3) or 30 deg.

answer is: x = 5pi/6 + kpi

2. 4(cos^2)x-1=0 -----> cosx = 1/2 or 60 deg.

answer is: x = pi/3 + kpi, 2pi/3 + kpi

3. 3(csc^2)x-4=0 -----> cscx=2/(sqrt3) or 60 deg.

answer is: x = pi/3 + kpi, 2pi/3 + kpi

.................

I can do all the algebraic steps, what I'm confused about is how did they come up with kpi as the answer shouldn't it be 2kpi?

because this is what i got...

1. [5pi/6 + 2kpi, 11pi/6 + 2kpi]

what I was thinking was that since tanx=-1/(sqrt3) I would need the solutions of the quadrant where tan is negative, which is quadrant II and IV

2. [pi/3 + 2kpi, 5pi/3 + 2kpi]

again, since cosx=1/2, which is positive...the solutions would be in quadrant I and IV

3...same idea, positive answer cscx = 2/(sqrt3)..solutions are in quadrant I and II

Please help, thanks!