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The Maclaurin polynomial of degree 5 for the function \(f(x) = \arctan(x)\) is$$ P_5(x) = x - \frac{x^3}{3} + \frac{x^5}{5} $$Use this polynomial and the fact that \(\arctan(1)=\frac{\pi}{4}\) to find an approximation for \(\pi\) (round to 3 decimal places).
\(\pi \approx\)