Determine all solutions of the equation: sec x + tan x = root 3

I put everything in terms of cos and sin and got:

1/cosx + sinx/cosx = root 3

1+sinx = root 3

sinx = root 3 -1

sinx = 0.73205

x= 47.06

Does anyone know if this is right so far? I'm not sure what to do next. The answers are in radians and laid out as follows: (k means all integers)

x= pi/6+2pi(k)

x= 5/6+2pi(k)

x= 2pi(k)

x= 7pi/6+2pi(k)

x= 11pi/6 +2pi(k)

Thanks so much for all help!