I would start by rewriting it in terms of the cosine function, since sec(x)=1/cos(x). Using this and doing a bit of rearranging makes the equation 3/cos^{2}(x)=4. Now divide both sides by 4 and multiply both sides by cos^{2}(x) to get cos^{2}(x)=3/4. This implies that cos(x)=\pm\sqrt{3}/2.
The solutions of the equation cos(x)=\sqrt{3}/2 are x=pi/6+2n\pi=30^{\circ}+360^{\circ}n for n=0,\pm 1,\pm 2, \pm 3,\ldots and x=-pi/6+2n\pi=-30^{\circ}+360^{\circ}n for n=0,\pm 1,\pm 2, \pm 3,\ldots
The solutions of the equation cos(x)=-\sqrt{3}/2 are x=(5pi)/6+2n\pi=150^{\circ}+360^{\circ}n for n=0,\pm 1,\pm 2, \pm 3,\ldots and x=(7pi)/6+2n\pi=210^{\circ}+360^{\circ}n for n=0,\pm 1,\pm 2, \pm 3,\ldots
