"Meanwhile, vacuum to waste and brush the pool once a day."

Be sure to follow up on this bit of advice, it's important to clearing up the water quicker. When you shock and kill the green algae, it is dead but still there. That's part of the cloudiness after wiping out the greenies and it's a lot of the fine residue on the bottom of your pool after the greenies are dead.

I opened to a green mess for the first time this spring and zapped the green stuff in about a day and a half with LOTS of 12% chlorine, then turned the pump off until the residue settled to the bottom and vacummed the junk to waste.