Its sine function!

Geometry Level 3

If sin9°=abaaϕaa\sin 9\degree = \sqrt{\dfrac{a-\sqrt[a^a]b \cdot \sqrt \phi}{a^a}} for positive coprime integers aa and bb, find the value of

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

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