Solve tan^2 x-3=0 for 0 is less than or equal to x which is less than or equal to pi

solve tan^2 x-3=0 for 0 is less than or equal to x which is less than or equal to pi

tan^2(x) - 3 = 0

Bring 3 to the right hand side.

tan^2(x) = 3

Take the square root of both sides.

tan(x) = +/- sqrt(3)

Which means we have two equations to deal with:
tan(x) = sqrt(3) or tan(x) = -sqrt(3)

Tan is equal to sqrt(3) at the points pi/3 and 4pi/3.
Tan is equal to -sqrt(3) at the points 2pi/3 and 5pi/3.

So there are four solutions, assuming the solutions lie between 0 and 2pi.
x = { pi/3, 2pi/3, 4pi/3, 5pi/3 }

tan^2 x - 3 = 0 iff
tan^2 x = 3 iff
tan x = +_ sqrt(3) iff
x = pi/3 or x = 2pi/3