Solve the equation for exact solutions in the interval $[0^{\circ },{360}^{\circ })$. Use an algebraic method.
$$6{\sec }^2\theta \tan \theta =8\tan \theta$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Do not include the degree symbol in your answer.)
B. The solution is the empty set.

Step 1 ：The given equation is $6{\sec }^2\theta \tan \theta =8\tan \theta$.

Step 2 ：We can simplify this equation by dividing both sides by $\tan \theta$, assuming $\tan \theta \ne 0$. This gives us $6{\sec }^2\theta =8$.

Step 3 ：We can further simplify this by noting that $\sec \theta =\frac{1}{\cos \theta }$, so the equation becomes $6\left(\frac{1}{{\cos }^2\theta }\right)=8$.

Step 4 ：Solving this for $\cos \theta$ will give us the solutions for $\theta$ in the interval $[0^{\circ },{360}^{\circ })$.

Step 5 ：The solutions obtained are in radians. We need to convert these to degrees to match the interval given in the question.

Step 6 ：We also need to consider the case when $\tan \theta =0$, which we initially assumed to be non-zero to simplify the equation. The values of $\theta$ for which $\tan \theta =0$ in the interval $[0^{\circ },{360}^{\circ })$ are $0^{\circ }$ and ${180}^{\circ }$.

Step 7 ：Combining all the solutions, we get $\theta$ = $0^{\circ },{30}^{\circ },{150}^{\circ },{180}^{\circ },{210}^{\circ },{330}^{\circ }$.

Step 8 ：Final Answer: The solution set is $\boxed{{\displaystyle 0^{\circ },{30}^{\circ },{150}^{\circ },{180}^{\circ },{210}^{\circ },{330}^{\circ }}}$.