Answer: We can simplify the expression as follows:
sin theta / (1 + sin theta) - sin theta / (1 - sin theta)
= [(sin theta)(1 - sin theta) - (sin theta)(1 + sin theta)] / [(1 + sin theta)(1 - sin theta)]
= [(sin theta - sin^2 theta) - (sin theta + sin^2 theta)] / [1 - sin^2 theta]
= -2 sin theta / cos^2 theta
= -2 tan theta
So the simplified expression is -2 tan theta, with no quotients.
Explanation: