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Having read the books several times now, one thing that just jumped out at me as unclear is why did Sansa need the hair net she wore to Joff's wedding?
I know that the hairnet was holding a Strangler crystal, but my point is why did they need to use that means to get the poison into the wedding feast?
Possibilities I've considered but can't find clear evidence:
1) The conspirators were trying to frame Sansa.
The problem with that is that I don't recall the Hairnet ever being notice as an attack vector.
2) The conspirators couldn't get the "tool" in place except by that means. The problem there is that there's no evidence that anyone was searched or otherwise prevented from bringing things other than obvious weapons into the wedding.
Overall, this approach seems to have increased the risk to the plan (maybe Sansa would decide not to wear it, maybe she would decide to mention the oddness to someone, it relied on bringing more folks into the conspiracy, etc), with little upside. So why bother?
EDIT: please note this is a book question. There seems little evidence in the books so far that Littlefinger and Lady Olenna had any contact on this subject before she came to Kings Landing from Highgarden. Littlefinger met Mace Tyrell in the field, not at his seat, while Margaery and Olenna came from Highgarden. Dontos gave Sansa the hairnet well before Olenna was even introduced as a character, and her characterization of Mace gives strong impression that he’s not a subtle or devious person, which makes it unlikely that he’d enter the betrothal with the intent to kill.