The Americans knew a lot was riding on a Sept. 11 meeting with the king of Saudi Arabia at his summer palace on the Red Sea.

A year earlier, King Abdullah had fumed when President Barack Obama called off strikes against the regime of Syria's Bashar al-Assad. This time, the U.S. needed the king's commitment to support a different Syrian mission—against the extremist group Islamic State—knowing there was little hope of assembling an Arab front without it.

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