$arctan(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{1+2n}{x}^{1+2n}=x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}+\frac{x^9}{9}-$cdots

add terms one at a time to estimate arctan$(0\mathrm{.}75).$ After each term is added, calculate the true and approximate

relative errors. Use your calculator for finding the 'true' value. Retain $5$ decimal places in your calculations.

Present your results in a tabular form like the one in Example $4\mathrm{.}1$ of the book. The template is given below,

partially filled. Fill in empty boxes and add rows if necessary. Continue your calculations until you achieve $2$

significant figures accuracy.

Note: The $e_a$ calculation in the first iteration cannot be done as at this point there is no previous approximation.

Hence, it should be left blank or filled with N$/$A$.$ The value of $e_t$ can still be calculated as the true value is known.