APT- Portfolio Management

Can someone explain me the logic behind these types of questions when we are given 3 portfolios along with their betas and expected return ? Im struggling.

I get that with APT we are trying to determine arbitrage opportunities. However, I do not get how we can determine if there is an arbitrage when we are given information to three portfolios with their corresponding betas and expected returns. Why do we create a forth portfolio and why do we choose the middle value of beta to create it? Lastly, how do we get to the weight? I am pretty confused on the whole logic

The idea is to create a portfolio with zero beta and see if it earns more than the risk-free rate; if so, there’s an arbitrage opportunity.