I agree that they are mostly unnecessary with only three people. But I'll have a stab at a blunt division of responsibilities:

- CEO: Main purpose is making sure that there is a company to run. Get funding etc.

- CPO: (I suppose you intent it to mean Chief Product Officer) Main purpose is to make sure you build a product that the market needs.

- CTO: Main purpose is making sure that the product can/will be build.