Implement a for loop (with break and else statement) to use this formula for calculating sin(x) and see if your calculation would get the accuracy of 0.000001 (compare with sin(x) value from the math library) for the given accuracy requirement. For each iteration, print the estimated value (i.e. calculation), the accurate value (i.e. use math library value math.sin(x)) and the difference. Break out your loop when reaching the required accuracy.

Use a while loop to include all test cases, i.e. a loop that asks user to continue to next test or to terminate.

Special note: in order to avoid overflow, please optimize your calculation, i.e. its improper to calculate 1! by 1 divides n! as n! may lead to overflow.

Required test runs:

The following 5 test runs plus 3 additional test runs of your choice.

(1) x = pi/3, (2) x = -pi/6, (3) x = 0.112, (4) x = pi, (5) x = pi/2 where pi value can be found at math library, plus at least two additional tests of your choice. You enter the input via an interactive user interface, i.e. given user choice to enter actual radius value or enter in pi format, i.e. for pi value, dont enter actual value, ask user to enter pi and then use math.pi value internally (feel free to design your own user-computer dialog.)

sin(x)=i=0(2i+1)!(1)ix2i+1=x3!x3+5!x57!x7+