Given that
\[\cos 2 \theta = \frac{1 + \sqrt{5}}{4},\]find $\tan^2 \theta \tan^2 3 \theta.$The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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