If
\[\frac{\sin^2 3A}{\sin^2 A} - \frac{\cos^2 3A}{\cos^2 A} = 2,\]then find $\cos 2A.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If
\[\frac{\sin^2 3A}{\sin^2 A} - \frac{\cos^2 3A}{\cos^2 A} = 2,\]then find $\cos 2A.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{4}
If
\[\frac{\sin^2 3A}{\sin^2 A} - \frac{\cos^2 3A}{\cos^2 A} = 2,\]then find $\cos 2A.$
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