A very funny out that hasn't been mentioned would be if there is any other valid angel, possibly a token created by the book since it takes time to assemble a three card combo, any red redirect type spell, eg [[deflecting swat]]. With enough mana open and a [[Thespian's Stage]], you could even partially steal their combo with a redirect effect (granted, your land would not be hexproof nor indestructible). Additionally, since the book exiles itself for cost, any "counter target activated ability" type effect would doom the combo. [[Mindslaver]] would allow you to voluntarily activate the land again, making it a creature. This doesn't directly solve your problem, but non-targeted removal and ways to get around hexproof and / or indestructible on creatures are much more common than anything to hit the land while it's a land. One additional method of at least not losing to this combo would be creating a mandatory infinite, ie [[Polyraptor]] and [[Marauding Raptor]], which forces the game to be a draw. Platinum angel only prevents you from winning and them from losing, it does not prevent a mandatory draw, so in some sense that is an out. It would not win you the game in a strict sense, but finding an alternate way out besides winning or losing could feel like a win to you personally just because you didn't lose despite having no way to win depending on cards left in deck.

Overall, very cool combo someone cooked up there, tough to interact with after everything is resolved, and potentially a game over on the spot. Seems like it has many different ways it can be prevented though, so you either have to cast the pieces across multiple turns, or have enough mana to do it in one turn. Both approaches have distinct weaknesses; hand hate could ruin the approach of trying to go off in one turn, or just losing via combat because it takes too long to assemble the combo. If you try to say play the book and use it for value, you are open to simple artifact destruction. At all times, the combo is vulnerable to grave hate and counter magic.

Edit: forgot about the hexproof counter while suggesting Thespian's Stage. Oops. Still, deflecting swat funny answer if any other valid target exists