00 In addition to the 'cos pre-defined function, which is found in the 'cmath' library, the cosine of an angle (given in radians), can be estimated using the following series: (-1) cos(x) = (2k)! k=0 The series can be written as: x2k x6 28 x2 cos(x) = 1 - + + 2! 4! 6! 8! Write a C++ program that reads a list of angles (in degrees) and the values of k (k represents the numb terms in the above series) from an input file called (angles.txt). The program should only accept angles between 0 and 180. When invalid angle is read from the file, an error message should be displayed (see the given sample output). e program should include the following user-defined functions: which is used to compute the the factorial to be used in the above series