First, if it had any poop in it, it is considered in some areas, hazardous medical waste. So you my want to check what the codes are in your area.
The air vent and the drain plumbing must be removed. Then the fasteners holding the tank in. You need to support the tank while doing this. The tank will then drop down and slide out so long as there is clearance. You may need two of you for this. No matter what the cost, I would have it done as to not deal with the contaminated tank. You cannot rinse a tank clean. Poop will remain in the bottom.