Given that
\[\cos 2 \theta = \frac{1 + \sqrt{5}}{4},\]find $\tan^2 \theta \tan^2 3 \theta.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Given that
\[\cos 2 \theta = \frac{1 + \sqrt{5}}{4},\]find $\tan^2 \theta \tan^2 3 \theta.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{5}
Given that
\[\cos 2 \theta = \frac{1 + \sqrt{5}}{4},\]find $\tan^2 \theta \tan^2 3 \theta.$
train