Prove that tFT$2$ tFT$1(1+$ T$1$rT$2)+$ T$1$CT$2$ using a pure arbitrage argument

where t is today, T$1$ and T$2$ are maturity dates and t $<$ T$1<$ T$2$

Ignore marking$-$to$-$the$-$market.

a$)$ What are some reasons that in reality this is not a pure arbitrage?

b$)$ How important an effect might these have on the arbitrage profit?

c$)$ Can you think of any way to get around these problems?