Finding all solutions to Trig Equations

I'm working on a few problems where I have to figure out all solutions to a given equation between [0,2PI). Here's one i got but i'm not all that sure that it is correct:

tan x ^ 2 - 2 tan x - 3 = 0

My Solution:

(tan x - 3) (tan x + 1) = 0

tan x = 3 , tan x = -1

Both have no solution.

I don't think this is right though, i've yet to solve any of these problems where i didn't find at least one solution. I'm guessing i would probably have to solve it another way correct?