For Holmes Beach or Anna Maria Island a simple approach to get around 10% accurate is to take the final sales price and multiply by 1.5%. So in your example .015 X $400,000 = $6000 for your property taxes. Of course not an exact figure but this will get you within about 10%.
You can contact the county tax appraisers office in 34217 zip code. They will be the ones setting the milage rate that is multipled by the sales price. Did you buy the home yet? I could look up last years tax bill so you will know what that is as a reference point.