"Part 3" is a side-short-story revolving around the kids (is my guess, the "next gen"). :| Lol
Another thing, the "Third eye" is not a Rinnegan, it's an eye containing the Sharingan's power hence the name Mugen Tsukuyomi. We don't even know if Sasuke's Rinnegan which is not the same as the Third Eye could cast Mugen Tsukuyomi.
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Also, take note that the eye of the actual pre-shinju Juubi is shown on the end cover and not the 9 Tomoe Sharingan oriented third eye which again negates the claim that Mugen Tsukuyomi is in effect. Even if it was in effect, nobody could break out of it so it wouldn't lead anywhere. :|
This is the second plotline that Kishi can take for a part 3. This can work with or without the Infinite Dreamworld plotline.
The Naga (One in Being) and The Garuda (One in Hearts)
The power of Rinne
What is the Power of Rinne (Transmigration) ?
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If you ask me it is the power of Choas.
Apparently it corrupts the Moon/Byakugan
Moon
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Byakugan
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Into the Sharingan / 3-Tomoed Rinnesharingan.
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Why am I calling the Sharingan a 3-Tomoed Rinnesharingan ?
Well, it's because the Sharingan's tomoe are connected with a circle. In most cases, the circle is blurred, but at high points of hatred it becomes clear.
Byakugan ---> Sharingan reference :-
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Which gets further corrupted into the 6-Tomoed Rinnesharingan.
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And even further corrupted into the 9-Tomoed Rinnesharingan.
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So, because of the power of Rinne, a cycle of corruption starts :-