Solve
\[2 \sin \theta (\sin 2 \theta + \sin 4 \theta + \sin 6 \theta + \dots + \sin 14 \theta) = \cos \theta - \frac{1}{2}\]where $0^\circ \le \theta \le 24^\circ.$  Enter all the possible solutions, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve
\[2 \sin \theta (\sin 2 \theta + \sin 4 \theta + \sin 6 \theta + \dots + \sin 14 \theta) = \cos \theta - \frac{1}{2}\]where $0^\circ \le \theta \le 24^\circ.$  Enter all the possible solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4^\circ, 20^\circ
Solve
\[2 \sin \theta (\sin 2 \theta + \sin 4 \theta + \sin 6 \theta + \dots + \sin 14 \theta) = \cos \theta - \frac{1}{2}\]where $0^\circ \le \theta \le 24^\circ.$  Enter all the possible solutions, separated by commas.
train