Excel in math, science, and engineering

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The value of \( \log_3 \frac{1+\tan(15^\circ)}{1-\tan(15^\circ)} \) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

This problem is posed by Meliton C.

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