Board Thread:Theories and Speculation/@comment-35448581-20160502192848/@comment-25122992-20160506171145

Yeah, Rinne Sharingan has nothing to do with the Byakugan, it's just the result of Kaguya consuming the Chakra Fruit and attaining the power of Shinju, i.e. the chakra itself. I'm not even sure that until getting the chakra, Ootsutsuki eyes had been any doujutsu at all. It's even possible that these were just regular eyes of the Ootsutsuki folk with no special abilities, yet in conjunction with chakra, they were turned into a real doujutsu. Thus, Kaguya gained two doujutsu powers with the Fruit: the power of the Shinju itself (Rinne Sharingan) and the power that awakened in her own eyes thanks to chakra acquirement (Byakugan). But I must note that these are only "eye" powers of Kaguya, she also got a lot of "body powers" (ash bones, rabbit needles etc). These "eye" powers were individually inherited by two children of her, yet while Hamura got his power with no changes (the same Byakugan as Kaguya's), another one (Rinne Sharingan) deteriorated/changed it's form into new doujutsu - Rinnegan of Hagoromo. At least the latter also inherited some Kaguya's "body" power in form of the Six Paths Senjutsu.

Sharingan, the eyes of Hagoromo's older son, is surely a deterioration of the Rinnegan cause "eye" and "body" powers of his were split between Indra and Asura and in their new forms were individually weaker than while combined within one person. Byakugan was separately spreading amongst Hamura's bloodline, and although some power deterioration probably happened, all Hamura's descendants (i.e. at least Hyuga and Ootsutsuki clans) possess this doujutsu in it's primary form.

So these are two separate "eye" powers who were passed down onto two different bloodlines, although one of them (Hagoromo's > Indra's) lost it's original strengh (when it was combined with "body power", i.e. existed as Rinnegan along with SPS) and manifested as some lesser doujutsu forms.

Edit: now regarding Tenseigan. Surely, it wasn't included in this sceme until the Last Movie. Yet it still should be taken into account. I have a clue that Hamura inherited some Kaguya's "body" power akin to Hagoromo's SPS as well, but it didn't manifest properly (while we can see Hamura with TSBs, we don't know where they actually came from), only with enough time passed Hamura was able to truly awaken it, thus advancing his Byakugan into Tenseigan. I think that all Hamura's descendants inherited at least some part of his hidden "body" power (for example, it's probably where that Hyuga chakra control ability comes from), although it was also split between Ootsutsuki and Hyuga clans, thus only a combination of these bloodlines power and their chakra allows to unlock Hamura's ultimate power, Tenseigan, again. It's what Toneri has done by getting Hyuga Byakugan and combining it's chakra with his own Ootsutsuki chakra.