The difference between those is that the first ones are simple prepositions, while the other are the preposition united with the article. So, generally, when you talk about something in general you use simple prepositions, when you talk about something specific you use preposition + article. (Mi immergo in acqua. Mi immergo nell'acqua della piscina). Tha same is for abstract concept as in yours examples. Parlare in modo distaccato is general while, when you say ho cercato di trattare nel modo più distaccato, you are suggesting a specific situation where you talked that way (this because of the verb tense).
If you have any other doubt don't hesitate to ask.