maximum value

I will assume that you mean

f(x) = sin3xcosx/(tan2x+1)    this has no global maximum   (ref: Wolframalpha)

so maybe you mean  

f(x) = (sin3xcosx/tan2x)+1       (yes I know this is how it should be interpreted bum a loy of people make mistakes here)

 

I spent ages working on the first interpretation,  I haven't got the energy to look at this second one at present but Wolfram Alpha says the maximum is  2.5