What happened at Mount Doom?

[mormegil]

I choose that Eru willed it because of one main factor. As I have stated elsewhere if there is anyone that had right to know the will of Eru it would be Manwe. Well Manwe wasn't in Middle-earth at the time but his servant was. That to me means that Gandalf, as Manwe's servant and obviously the most "righteous" of the Istari, would be the logical choice for the recipient of what Eru's will would be. I believe he knew a bit of the will of Eru when he said

I have not much hope that Gollum can be cured before he dies, but there is a chance of it. And he is bound up with the fate of the Ring. My heart tells
me that he has some part to play yet, for good or ill, before the end; and
when that comes, the pity of Bilbo may rule the fate of many - yours not
least.

It is obvious here that Gandalf has some inkling here of Eru's will though he knows not what part Gollum will play he knows that Eru's will is set that Gollum will play a part.

And I don't believe that this makes Eru a murder in the least. His will is divine and without fault. Therefore when he gives life it's also his to take away whenever he deems it fit.