how to replace #3 ignition coil on 2002 camry

You do not have to remove the manifold, definite not. You disconnect the electrical connector and its difficult to get at but remove the 10mm bolt securing the coil to the valve cover. you may need a stubby 10mm or even put a cheap 10mm box wrench in a vise and cut it with a hacksaw but it can be replaced in 15 to 20 minutes.