Write a Fortran program that prompts the user for x (as a double-precision real) and the highest order term, m and reports the approximated value of arctan(x) (as a double-precision real) using a counting loop. Some notes: To declare a Fortran double-precision real, use the REAL(8) data type, e.g. real(8):: sum, x ! sum and real are double precision floats Related note (but not needed here): Normal Fortran integer variables can hold values up to ~2 billion. To declare Fortran integers large enough to hold larger values (such as the results of a factorial), one might use 8 byte integers. They can be declared as follows integer(kind=8):: VarName ! VarName can hold larger values Caution must be paid in using reals versus integers. If your results seem off, this is a likely cause. Note that, since the tangent of pi/4 (45^degree) is 1, we can use 4 tan^-1(x) = pi as an easy check on how close the approximation is getting. Of course, it is also easy to check using a calculator. (The filename should be hw05_02. f 95.) Create a revised version of your code from 2) so that it asks for x but does not ask for the highest order term, m. Instead, it iterates enough times so that the absolute value (try Fortran's abs function) of the approximation of arctan(x) has changed by less than some tolerance, which you declare as a constant. This is best done using a do whi1e loop or a do loop with a conditional exit statement. For testing, report the approximated value and the number of iterations to find arctan(1) using tolerances of 10^-2 and 10^-3. (The filename should be hw05_03. f 95.)