# Its sine function!

Geometry Level 3

If $\sin 9\degree = \sqrt{\dfrac{a-\sqrt[a^a]b \cdot \sqrt \phi}{a^a}}$ for positive coprime integers $a$ and $b$, find the value of

$\log_a \left(\dfrac{80 \sin(3ab\degree)}{b} \right)$

Notations:

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