If
\[k = \sin^6 \theta + \cos^6 \theta = \sin 2 \theta,\]then find $k.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If
\[k = \sin^6 \theta + \cos^6 \theta = \sin 2 \theta,\]then find $k.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{2}{3}
If
\[k = \sin^6 \theta + \cos^6 \theta = \sin 2 \theta,\]then find $k.$
train