This can't be pretty

Algebra Level 5

If the expression

\[(\text{cis}(3))^{\cos^{-1}\left(\frac{3}{5}\right)}\]

Can be represented as \(\dfrac{-a}{b}+\dfrac{c}{b}i\) for positive coprime integers \(a,b,c\), find \(a+b+c\).

Details and assumptions:

It's up to you to decide whether the measurements are in degrees or radians :P

\(\text{cis}(\theta)=\cos(\theta)+i\sin(\theta)\)

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