Let's analyze and solve the problem:

We are tasked with solving $8 \tan \theta = 0$ for $0^\circ \leq \theta < 360^\circ$.

Step-by-Step Solution:

1. Simplify the equation: $8 \tan \theta = 0 \implies \tan \theta = 0$

2. Recall the property of the tangent function: $\tan \theta = 0 \text{ when } \theta = 0^\circ, 180^\circ, 360^\circ, \dots$ Within the interval $0^\circ \leq \theta < 360^\circ$, the solutions are: $\theta = 0^\circ \quad \text{and} \quad \theta = 180^\circ$

3. Check the given answer choices: The correct option is $0^\circ, 180^\circ$.

Final Answer:

$\boxed{0^\circ, 180^\circ}$

Would you like further clarification or additional practice?

Related Questions:

1. What is the period of the tangent function?
2. How do we solve trigonometric equations involving tangent?
3. What are the values of $\tan \theta$ at $90^\circ$ and $270^\circ$?
4. How does the unit circle help in solving $\tan \theta = 0$?
5. Can $\tan \theta$ have negative values? If so, when?

Tip:

For trigonometric equations, always consider the domain and periodicity of the trigonometric function to ensure you capture all valid solutions!