While the tub and sink are empty and dry, pour a cup or so of baking soda down both drains. Use a skewer or a chopstick to get as much of it down the drains as possible. Then pour a liter or so of HOT vinegar into each drain.
Don't be surprised if enough hair to make a wig starts bubbling up.
Pull it out and toss it in the trash.
Use a hair screen over the drains for all future showers.
There is also an inexpensive plastic gizmo that can be used to drag hair and sludge from the pipe.
http://www.kk.org/cooltools/archives/000507.php
(I have no monetary interest in this product. I am just a satisfied user.)
Shampoos, conditioners and moisturizers love to get together and hang out. Regular (monthly) baking soda/vinegar treatments can keep your drains flowing.