Compute
\[\cos^3 \frac{2 \pi}{7} + \cos^3 \frac{4 \pi}{7} + \cos^3 \frac{8 \pi}{7}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute
\[\cos^3 \frac{2 \pi}{7} + \cos^3 \frac{4 \pi}{7} + \cos^3 \frac{8 \pi}{7}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-\frac{1}{2}
Compute
\[\cos^3 \frac{2 \pi}{7} + \cos^3 \frac{4 \pi}{7} + \cos^3 \frac{8 \pi}{7}.\]
train