The Taylor series expansion of tan$1$ for $||<1$ is: Develop an algorithm that performs the following $($you can present it in the form of a pseudo$-$code or a list of steps$)$: The algorithm determines tan$1$ using the above equation, where the argument x is the input, and the output argument y is the approximate value for tan$1$ obtained using Taylor$$s series expansion. If $$ is the nth term of the series, then sum $$ of the first n terms is $=1+.$ In each pass, calculate the estimated error E given by $=||.$