Its sine function!

If \(\sin 9^\circ=\sqrt{\frac{a-\sqrt[a^a]{b}\cdot\sqrt{\phi}}{a^a}}\) for positive coprime integers \(a\) and \(b\) find \[\log_a\left(\frac{80\sin\left(3ab^\circ\right)}{b}\right)\] **Notation:** - \(\phi=\frac{1+\sqrt{5}}{2}\) is the Golden Ratio