I removed mine not all that long ago. It was quite tricky.
First, having a manual is always a joy. I hope you have the "Standard Triumph" Workshop Manual.
a) Remove the dash hardware that fastens the windshield to the dash scuttle, the three chrome bolts, etc.
b) Remove the nuts from the bottom of the posts in each wheel well. Easy.
c) Loosen the two bolts visible on each side, 4 total, when each door is opened. You'll see the bolts there, and be careful not to strip the heads.
d) The Manual says you can now pull the windshield up. You can't. With the lower nuts removed, and the two bolts on each side loosened, you're still nowhere if you have the typical TR4. The frame posts will be frozen by stubborn age into the slots on the two mounting brackets. Pulling the windshield may well be fruitless (unless luck lends a hand).
e) Use liberal amounts of WD-40 or penetrating oil, avoiding ruining your carpet or paint. Then, assuming I'm correct that loosening the side bolts did nothing, you should actually remove those side bolts, careful not to lose any hardware, and with a wrench or other tool, perhaps with a rag to avoid ugly marring of the steel, rotate those oiled up mounting brackets back and forth, back and forth on the windshield posts until they actually slip around a bit. Then either just slide the brackets off, and with a helper pull the windshield evenly out of the car, or reinstall the brackets loosely with the bolts again, and then remove the windshield with a helper.
This is just a long way of saying that those side brackets (post holsters) are a hassle after age, and you'll need to be creative.
Good luck.