Sims 3 camera - rotate without using the keyboard?

If you're using a mouse, hold down the middle mouse button and move the mouse around. This rotates in any direction you want, not just a simple rotation left or right, so it may take a bit of finesse to keep the angle where you want it.

If you're using your laptop's touchpad, you may or may not be able to configure it to do what you want:

https://pcsupport.lenovo.com/us/en/videos/vid500008