It is hard to cut tube at the right angle when you do not have specific equipment. This method is well known and give nice result, the only painfull task is to get the right paper layout of your cut. Therefore I made a little online tool to do so.
In the middle of the page, url here under, you will have to enter millimeter for diameter of the tube and angle in degree and then click to generate a pdf file.
Before printing the pdf be sure that the document will not be scaled by your computer, you would loose the correct dimensions.
Step 1: Using the Layout
Cut and tape the layout to the tube, keep a rectangular shape under the sinus curve, it will help. If everything is ok the end and the beginning of the curve meets each other around the tube.
Mark the border of the curve. Measure once again, one more time and an other time, and if it seems ok to you then cut.
After that I made the cut with a hand metal saw wich is not very precise. But the result is quite ok, I think a welder could work with the little gaps.
In conclusion nothing new, just an automated calculation and my first instructable :)
Thanks for your remarks and do not mind arguing about my bad english writting.