I don't understand how to prove that each side equals each other

(sinθ/1-cosθ) + (1-cosθ/sinθ) = 2cscθ

Get a common denominator (sinθ)(1-cosθ) for the fractions on the left. Then the numerators of fractions of the left will add to (sinθ)(sinθ)+ (1 - 2cosθ + (cosθ)(cosθ))= 2(1-cosθ) so the added fractions simplify to 2/sinθ. This is just 2cscθ