How Does SO3 Form 3 Pi Bonds Without an Expanded Octet Structure?

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Since SO3 has an expanded octet structure, the central S should form three double bonds with O, meaning S forms 3 pi bonds in total. However, after hybridisation of S, there are less than three unpaired electrons in unhybridised p-orbitals of S. How can S form 3 pi bonds when there aren’t enough electrons from unhybridised p-orbitals? Thanks.
 
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SO3 does contain three double bonds with O. Sulfur is SO3 is sp2 hybridized. I count six electrons? And of course two for each oxygen atom for a total of 12 electrons in the system.

Did I misunderstand your question?
 
There is no such thing as "expanded octet structure" in main group element chemistry. This has long been disproven. So at most one double bond, which may resonate between the different O-atoms.