What color do you mix to tan paint to get gray paint?

It depends on the particular hue of tan, but assuming it's a typical yellowish tan you would mix it's compliment (a muted bluish purple) to get gray. To get grey or brown you always mix complimentary colors. If you want brown you use a bit more of the warmer hue in the complimentary pair. If you want grey, you use more of the cooler hue.

Compliments are generally:

red & green

orange & blue

yellow & purple/violet