Start with the Engineer's calculator, Microsoft Excel. Or your favorite spreadsheet program.
Plot out your current trapezoidal modulstion. Then add the ideal sine wave on top of that. Calculate the difference between the ideal sine and the trapezoid.
You should find that the error is small. Maybe only a few percent.
I assume your power supply has a limited voltage? With that limit appled to a sine wave, you will see that you only give full voltage to the motor for a very short amount of time in each cycle. The trapezoid gives the motor more power for longer.
Then ask yourself if there is any benefit in using the sine wave.