You won't believe how well this works, and I just "made it up" myself.

Wet the tub surface, squeeze on a generous amount of Dawn liquid dishwashing detergent and then shake on a good amount of Comet powered cleanser right on top of the Dawn.

Mix the Comet with the Dawn using a scrub brush (don't scrub it yet) and let the mixture sit for 30 minutes or more.

NOTE: Make sure any pets or kids are not allowed near the tub while the mixture sits.

Come back and scrub the mixture away (no need to scrub too hard) as you rinse with clean water.

The dark "stains" (just greasy dirt, really) will be gone!