I would have suggested having 2 zones per tile: one to rotate left, one to rotate right. But the tap zone is quite small already, so it's prone to errors. One

I would have suggested having 2 zones per tile: one to rotate left, one to rotate right. But the tap zone is quite small already, so it's prone to errors. One slower but more UX-friendly option would be to allow long-press on a tile, it would zoom in, and you can pick left or right with each button. Double tap is also an option but you need to remove the ability to select the content of the page.