Compute:
\[
\sin \frac{\pi}{12} + \sin \frac{3\pi}{12} + \sin \frac{5\pi}{12} + \sin \frac{7\pi}{12} + \sin \frac{9\pi}{12} + \sin \frac{11\pi}{12}.
\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute:
\[
\sin \frac{\pi}{12} + \sin \frac{3\pi}{12} + \sin \frac{5\pi}{12} + \sin \frac{7\pi}{12} + \sin \frac{9\pi}{12} + \sin \frac{11\pi}{12}.
\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{2} + \sqrt{6}
Compute:
\[
\sin \frac{\pi}{12} + \sin \frac{3\pi}{12} + \sin \frac{5\pi}{12} + \sin \frac{7\pi}{12} + \sin \frac{9\pi}{12} + \sin \frac{11\pi}{12}.
\]
train