Sonna = such a/an ~ , like that .
koto = thing
iu = say / tell
nante = ( suru ) nante = how dare ~ in annoying situation , or the phrase literally follows as a suffix of all verb(in this case , IU is the verb) when you were surprised at the thing someone did without anger .
Whether you are annoyed , angered , or simply surprised depends on context.
Good luck :))))