Hybridization Involving Tryptophan

[704578485]

I was just going over the 2011 Midterm and am having a lot of trouble with question 6c. I understand why the carbon atoms' hypridozation is sp2. However I am having a lot of trouble seeing why the Nitrogen and Oxygen atoms have an sp3 hyribidization.

[Alli Foreman 2H]

This structure is drawn differently from those we usually do in that it doesn't show all the hydrogen atoms or all the lone pairs. The problem states this (it's usually done just to save space/time).

In this case, N is bonded to two hydrogen atoms, one carbon atom, and then it also has a lone pair to finish off its octet. Since it has four regions of electron density it is sp^3
Oxygen is bonded to one hydrogen atom, one carbon atom, and then has two lone pairs to finish off its octet. Since it has four regions of electron density it is sp^3