The anime just glossed over it with some subtle imagery, but in the novel it's stated that Kagenui had to take her time and unfold every single piece of the one thousand cranes to find the message about the shrine in one of them. She then explains that such inefficient method of leaving a message is precisely the warped aesthetic sense she was talking about, in her words: "It’s a question of patience. The pursuit of efficiency alone is hollow, and it ain’t no picnic to make one of these, a string of cranes. Tadatsuru made these all himself".
This gives us better insight on how we should expect him to act and is much less vague than leaving it at "he operates in a sense of aesthetics" like the anime does.
Now, when they first appeared in Nise, I talked about how the names of Yotsugi and Yozuru relate to each other, being literally a way to read "cotangent" and "cosine", well, Tadatsuru is not excluded from that, and his name is "sine". So, cotangent=cosine/sine; Ononoki equals Kagenui over Tadatsuru.
There's also a bit that was translated a bit weirdly in the subs: at some point, they wrote that Araragi said Tadatsuru was like "the perfect specialist", but the correct affirmation should be that he was "the perfect specialist for that situation", the perfect guy to go against them, hence why it felt too much of a coincidence.
About the next season to come: if you want to follow the novel release, the next one up should be Koyomimonogatari, followed by every Owari season as a single set, BUT I'll say that for this case specifically I feel like the pacing is better if you stick to the anime order and watch Owari > Koyomi > Owari S2
Whichever order you pick, I'll let you know the Koyomimonogatari episodes are 10 minutes long in average and they are better if watched in pairs :)
![Judgment Commentary! | Tsukimonogatari | Episode 3 "Yotsugi Doll, Part 3" [Reaction + Discussion]](https://img5.samukata.com/storage/1/hc/jx/4e9b88-019e8309-5d5f-7b55-ab3e-17c029e349d2.jpg)
