Do you know what distribution that mgf belongs to? That's step one. The sum of three independent rvs with that distribution also make a known distribution.

Actually... Were you told to use markovs inequality? Because I guess you wouldn't explicitly need to figure out what distribution that is for if that's the case.

This is almost definitely homework. Don't do all of their work for them. Plus my question is very relevant and although your approach is correct it probably isn't what their professor is going for.

To get an exact answer it won't. But you can use the information provided to get what you need to put a bound on the probability even without identifying the distribution. So yeah... Let's see if they were instructed to use markovs inequality.