Being able to key in an exact angle would be cool, but this would also be solved by implementing the more popular suggestion of a slider for day/month/year in addition to time.
It could also be done by allowing the user to "grab" the sunrise/sunset lines and drag them to a desired sun angle. The only catch is that the same sun angle occurs twice a year - so you'd have to be able to specify which date(s) were intended.
SunCalc
All the ideas and discussions