Take Taoyuan MRT to A1 (Taipei Main Station), check timetable here.
Take MRT to Jiantan Station, check timetable here.
Take bus R5 or bus 303 to Chinese Culture University (arould 35 minutes, TWD 15).
Take MRT from BR13- Songshan Airport to R10-Taipei Main Station.
Take MRT to Jiantan Station, check route map here.
Check transportation information here.