How did Madara really obtain his Eternal Mangekyou Sharingan? Regarding Madara's Eternal Mangekyou Sharingan, there are three canon stories on how he obtained it.

The first version is mentioned by Itachi, while explaining the Mangekyou to Sasuke. In this version, he tells that Madara took his brother's eyes. Itachi shows the scene to Sasuke through Genjutsu, where Madara places his fingers over Izuna's eye and Izuna is surprised by the action. This would mean a forceful extraction.

The second version is told by Obito, acting as Madara. He explains to Sasuke that Izuna willingly gave his eyes to him (Madara), to protect the clan from the dangers of the fame.

The third version is told by the First Hokage, Hashirama Senju, when he was reincarnated by Orochimaru. He tells that Izuna succumbed to the wounds (during the warring period) caused by Tobirama Senju. And it is assumed that Madara took his brother's eyes after he died.

So which version is the actual one? Or is it a mix of all three?
Based on the data that is provided by the story, we don't have enough information to make a deduction. The only witnesses to the event were Madara and Izuna.

While this means that Madara's account has greater credibillity than anyone else, Madara has a reputation for deceiving people, such as Obito, with complex webs of lies and staged events. As a result, we cannot consider him a reliable information source.

However, based on information provided in the Naruto Data Book (Number 4, page 37) on Izuna, Izuna gave his eyes willingly. So we can conclude that Madara was telling the truth, at least in this case.

For access to the Japanese data book I reference: https://www.reddit.com/r/Naruto/comments/2l976c/spoilers_the_complete_4th_databook/

For the translation:
https://aminoapps.com/c/anime/page/blog/naruto-data-book-izuna-uchiha/WltX_uRVgmj1rLGwaPw7envXJ0MEjo