Nagato has absolutley no way of breaking out of tsukuyomi evan if he does hell be practically braindead. 1 second in the tsukuyomi = 72 hours
if nagato manages o break out of it in half a second thats 42 hours of torture which he cant without sharingan anyway
Dude hes called Pain lol he would probaly enjoy it as i said before there are 3 ways to break out of genjutsu
How genjutsu works
the user has to manipulate the flow of chakra in the enemy's body causing disrutition in there brainwaves and all 5 senses are affected. however this can only work on the human brain.if cast corectly the user can manipulate the chakra flow through the celebrel nervouse system it can lead to causing the victim pain (because the brain thinks the body is in pain)
Fighting Genjutsu .
before you can do this you must relise you are in a genjutsu.
the first option is to break chakra control by disturbing the flow of your own chakra or someone else disturbing your Chakra.(sakura did this in the chunnin exams)
the second option is to cause pain to yourself regaining the 5 senses or another causing pain to you. (kurenei did this against itachi)
the 3rd option is to see through the illusion relying on your eye type or chakra control it is debated wether the rinnegan can see through sharringan genjutsu but the sharringan is good at seeing through gejutsu .
also Deidara trained his eye to see through genjutsu (unexplained).