cos(3x)/cos(3x)+ sin(3x) + cos(3x)/cos(3x)-sin(3x) = 3

pi, NOT pie!

If you mean
cos(3x)/(cos(3x)+ sin(3x)) + cos(3x)/(cos(3x)-sin(3x)) = 3
then
cos(3x)(2cos(3x)) = 3(cos^2(3x)-sin^2(3x))
2cos^2(3x) = 6cos^2(3x) - 3
cos^2(3x) = 3/4
cos(3x) = ±√3/2
3x = ±π/6+2kπ/3, ±5π/6+2kπ/3
pick values of k that put x in [-π/2,π/2]