The convergent series

known as the Madhava$$Leibniz series, can be used to estimate

to an arbitrary level of precision. The formal definition of the series reads as follows:

where each

is given by:

Write a code that approximates

using the Madhava$$Leibniz series. It should start by setting the total sum $($mysum$)$ to zero, and then proceed to add a new term

to mysum in each iteration of a while loop. It should stop when the absolute value of

becomes smaller than the given

$.$