Verified answer

                 sec²x = 3 tanx

              1 ⁄ cos²x = 3 sinx ⁄ cosx

... as a rule I don't cancel terms on each side of an equation. In this case it

doesn't matter.

        (1 ⁄ cos²x) – (3 sinx ⁄ cosx) = 0

           (1  –  3 sinx cosx) ⁄ cos²x = 0

               1  –  3 sinx cosx = 0

         1  –  (3 ⁄ 2)2 sinx cosx = 0  ...  sin(2A) = 2 sinA cosA

             1  –  (3 ⁄ 2)sin(2x) = 0

                   sin(2x) = 2 ⁄ 3

                    2x = 41.81º, 138.19º, 401.81º, 498.19º

                     x = 20.9º, 69.1º, 200.9º, 249.1º