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.)