Add the required amount of shampoo to the toilet water, and put both lids up.
Pick up the cat and soothe him while you carry him towards the bathroom.
In one smooth movement, put the cat in the toilet and close both lids. (You may need to stand on the lid.) The cat will self agitate and make ample suds. (Never mind the noises that come from the toilet, the cat is actually enjoying this.)
Flush the toilet three or four times. (This provides a "power-wash" and "rinse".)
Have someone open the door to the outside (Be sure that there are no people between the toilet and the outside door.)
Stand behind the toilet as far as you can, and quickly lift both lids.
The now clean cat will rocket out of the toilet, and run outside where he will dry himself off. The toilet will be sparkling clean!