# How's this related to trig?

Calculus Level 5

$\dfrac{7}{5} = x + \dfrac{x^2}{2!} - \dfrac{x^3}{3!} - \dfrac{x^4}{4!} + \dfrac{x^5 }{5!} + \dfrac{x^6}{6!} - \dfrac{x^7}{7!} - \dfrac{x^8}{8!} + ...$

If the value of $$x$$ that satisfies the above equation can be expressed in the form $$2 \arctan \left( \dfrac{-a + \sqrt{b}}{c}\right) + 2\pi k$$ for integer $$k$$, with where $$a$$ and $$c$$ are positive coprime integers and $$b$$ is square-free, find $$a + b + c$$.

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