Find all solutions of the equation in the interval [0, 2π). (enter your answers as a comma-separated list. if there is no solution, enter no solution.)
4 sec2 x + 2 tan2 x − 6 = 0

4sec^2(x)+2tan^2(x)-6=0
using 1+tan^2(x)=sec^2(x)
4(1+tan^2(x))+2tan^2(x)=6
4+4tan^2(x))+2tan^2(x)=6
6tan^2(x)=6-4=2
tan^2(x)=1/3
tan(x)=sqrt(1/3)=1/sqrt(3)=sqrt(3)/3
x=atan(sqrt(3)/3)=pi/6=30 degrees
However, tan(x) is a periodic function with period pi, therefore
the solutions are pi/6, pi/6+pi, or
{pi/6, 7pi/6}

To the risk of sounding redundant