# Trigonometry in Algebra 2

Algebra Level 5

$$\sqrt[3]{{\displaystyle\frac{{{x^9} + 9{x^2} - 1}}{3}}} = 2x + 1$$

$$x_1,x_2,...,x_n \in \mathbb {R}$$ are the solutions of this equation.

Let:

$$\displaystyle\frac{1}{\pi }\sum\limits_{i = 1}^n {\arccos \displaystyle\frac{{{x_i}}}{2}} = \displaystyle\frac{a}{b}$$

If $$a,b \in \mathbb {Z}, \gcd (a,b) = 1$$, find $$a+b$$

Hint: Some calculus needs to be applied.

This problem is part of this set

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