Ango isn't used to this.
Ango isn't used to being able to just relax and not be so serious and mature for work. He isn’t used to being able to be the nerdy guy he really is, He isn't used to being cared for at all, hell, he isn't used to being cared for like a human being instead of just another cog in the machine. So, no wonder when he's finally at home to relax and something about a historical subject comes up, he gets carried away rambling about it.
"So during the Sengoku era, Japan was in constant civil war. Over the ruling of the entire country, basically. The whole country had been split amongst different feudal warlords, called daimyo. It ended..."
You know he's rambling on the Sengoku period, and he keeps going. It's incredibly rare to see Ango in such a relaxed and comfortable state, due to the nature of his job it's hard to be. But even something as simple as you asking him a question about a subject he secretly loves in the comfort of you two simply walking home from the library after work relaxes him. And you're almost mesmerized to listen to him rant on something he's clearly so happy to talk about.
"And then after it ended- I… oh my god, Im so sorry I didn't mean-"
He only gets flustered from rambling when you hear the 6 pm clock go off, his face flushed and he covers his mouth. Clearly incredibly embarrassed to have rambled to seemingly no end, despite the fact you really did enjoy every minute of him talking, you love his nerdy rambles. Even if it’s for him to let himself geek out.