Hi,
First or all I am not a plumber, but I had a similar problem..I also tried the plunger and chemical thing..this is what finally worked for me and I did it myself .
In the basement there is a plastic trap which comes off the bathtub drain, basically just a staright pipe with a u-shaped pipe connected to it, I simply unscrewed the pipe and found it full of hair and muck, I cleaned out the pipe about 6 months ago and never had a problem since.
If you plan on trying it yourself make sure you have a bucket ready when you unscrew the pipe, cause it is a nasty smelly job. also if the pipe is not plastic I would call a plumber..
Be carefull and take your time, hopefully you dont have a finished basement and can see the bathtub drain.
As far as your plumber saying the angle of the pipe is wrong, thats BS totally, If it drains after you plunge or put chemicals tells you it is not an angle problem..A plumber friend of mine told me long ago.."if it drains ok once, then the angle is good" in other words if the angle was wrong it would have NEVER worked since they installed the tub.
P.S...my tub also had a screen on the drain in the tub itself and was held on with 2 screws, When I removed the screen it was also clogged with hair.
good luck