TL;DR: Use a Mouse with a Polling Rate of 1000Hz.

It turns out that even if you play with 999FPS, that alone isn't enough to give you increase in speed. You also need to have a Mouse with the proper Polling Rate (Hz).

For example, if you play with 200FPS but use a mouse with 100Hz, the game will still only change your angle 100 times per second. If you have 300FPS + 100Hz or 100FPS + 300Hz, the game can still only notice your change of angles at 100 times per second. You are both limited by the game's FPS and your mouse Polling Rate.