2 Pre Calc Questions on extracting square roots and plugging in an angle

[benlangdon]

pre calc question in chapter 5.3 of Pre calculus seventh edition larson

solving trigonometric equations

solve the equation
3sec^2 x - 4 = 0


so i got secx = ±2 / √3

when i find out what angle it is with a graph do i have 4 angles?
like secx = 2/√3
which would be in the first quad and an angle of π/6 (30º)
and in the 4th quad and an angle of 11π/6 (330º)

then also have sec x = - 2/√3
which would be in 2 and 3 rd quad and be 5π/6 (150º) and 7π/6 (210º)

the answer is only π/6 and 5π/6
why?

i looked in the examples and they only do a square root problem with tan.
which is obviously only a period of π so that eliminates 2 of them.



any help would be great.
i am getting very frustrated.
and i have another question also.




i am supposed to verify that the x values are solutions of the equation.
they give 3tan^2 x - 1 = 0
and want to solve for
A. x = π/12
B. x = 5π/12

i have no idea how to solve this.
i mean i know you plug it in.
and you get 3tan^2 π/12 - 1 = 0
then 3tan^2 π/12 = 1
then tan^2 π/12 = 1/3
then im guessing
tan π/12 = √1/√3
now what?
besides rationalizing the denominator.