Answer:
   1
Step-by-step explanation:
Use the form for the factoring of the sum of cubes.
To make this easier to write, we'll use the substitutions ...
   a = sin(θ), b = cos(θ)
It looks like you may want to simplify ...
   (a³ +b³)/(a +b) +ab
   = ((a +b)(a² -ab +b²))/(a +b) +ab
The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...
   = (1 -ab) +ab
   = 1
   