Agree mostly with Bein Hasdorim. However there is no obligation to say modim derabanan. Only that when the tzibur is saying modim, if you do not bow and give hodaah, you are considered to be a kafui tova. MOdim derabanan is a collection of the various shitos of what should be said at that time. But if one is saying tefila, and is anyway bowing and saying the regular nusach of modim together with the tzibur, then there is no concern about missing the modim derabanan.
