QE$1-03$: The Maclaurin series expansion for the arctangent of $x$ is defined for $|x|1$ as

$arctan(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{2n+1}{x}^{2n+1}$

Estimate the value of $arctan(\frac{}{6})$ using the first $5$ terms of the sum. Develop an appropriate algorithm and code using for$-$command. Print the estimated value as well as the value produced by the builtin function atan for comparison.