Worrking from 'below the canopy of the umbrella' I would just take out any old, damaged or crossing branches, removing them from the centre of the canopy, and then I would remove the tips of any branches touching the ground. I would then stand back and identify any branches spoiling the outline or symmetry.
Apart from that I'd leave it alone.
“I am not lost, for I know where I am. But however, where I am may be lost.” Winnie the Pooh
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Apart from that I'd leave it alone.