Solve the equation for exact solutions over the interval $\left[0^{\circ}, 360^{\circ}\right)$.
\[
6 \sin \left(\frac{\theta}{2}\right)=6 \cos \left(\frac{\theta}{2}\right)
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is $\{$ \}
(Type an integer or a decimal. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma fo separate answers as needed.)
B. The solution is the empty set.

Step 1 ：The given equation is \(6 \sin \left(\frac{\theta}{2}\right)=6 \cos \left(\frac{\theta}{2}\right)\). We can simplify this equation by dividing both sides by 6, which gives us \(\sin \left(\frac{\theta}{2}\right)=\cos \left(\frac{\theta}{2}\right)\).

Step 2 ：We know that \(\sin \left(\frac{\theta}{2}\right)=\cos \left(\frac{\theta}{2}\right)\) when \(\frac{\theta}{2} = 45^\circ\) or \(\frac{\theta}{2} = 225^\circ\), because \(\sin 45^\circ = \cos 45^\circ\) and \(\sin 225^\circ = \cos 225^\circ\).

Step 3 ：So, we can solve for \(\theta\) by multiplying both sides of the equation by 2. This gives us \(\theta = 90^\circ\) and \(\theta = 450^\circ\). However, since we are looking for solutions in the interval \([0^\circ, 360^\circ)\), we discard the solution \(\theta = 450^\circ\).

Step 4 ：Therefore, the solution to the equation is \(\theta = 90^\circ\).

Step 5 ：Final Answer: The solution set is \(\boxed{90}\).