Answer
$$\tan \theta = \frac{{\sqrt {{x^2} - 64} }}{{\text{8}}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}x = 8\sec \theta ,{\text{ then }} \cr
& \sec \theta = \frac{x}{8} = \frac{{{\text{Hypotenuse}}}}{{{\text{Adjacent side}}}} \cr
& {\text{Opposite side}} = \sqrt {{x^2} - {8^2}} = \sqrt {{x^2} - 64} \cr
& \cr
& {\text{Express }}\tan \theta {\text{ in terms of }}x \cr
& \tan \theta = \frac{{{\text{Opposite side}}}}{{{\text{Adjacent side}}}} \cr
& \tan \theta = \frac{{\sqrt {{x^2} - 64} }}{{\text{8}}} \cr} $$
