# Sine of Arcsine Arctangent Sum

Geometry Level 2

Let $$x = \sin\left(\sin^{-1} \left(\frac{3}{5}\right) + \tan^{-1} (2)\right)$$. $$x$$ can be written in the form $$\frac{a\sqrt{b}}{c}$$, where $$a, b$$ and $$c$$ are positive integers, $$a$$ and $$c$$ are coprime and $$b$$ is not divisible by the square of any prime. What is the value of $$a+b+c$$?

Details and assumptions

$$\sin^{-1}$$ and $$\tan^{-1}$$ represent the inverse of the $$\sin$$ and $$\tan$$ function, and not the reciprocal.

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