The connection between F (frequency in Hz) and (rad/s) is . If you replace by in the formula for the phase, you get
. . . . .
That is the formula for the phase in terms of F, R and C. Notice that if then the denominator of the big fraction will be zero, so the phase will be " of infinity", namely a right angle (90 degrees or radians). That is what happens for the numerical values of F, R and C that you give.
If you are doing this on an Excel spreadsheet, you will need to check whether the function gives answers in degrees or radians. (I don't use Excel at all, so I have no idea how it copes with inverse trig functions.)