Go through your results for flights to Rio Branco in Brazil with Netflights. Although TAM usually has the best prices, it's best to double check what's available for your travel dates.
If these flights are too expensive, try searching for a different time of year. So if your dates are flexible, consider looking at different times of year.
So, if the flights to Rio Branco don't work for you, you could always try searching for flights to other airports in Brazil.
You can also broaden your search by looking at more than one departure airport. Have a look around – you might be able to save by flying from a different airport or city.