The question here is how is sin θ = sin (180 – θ).

This is based on mathematics trigonometry allied angles rule. If θ is an angle, then – θ, θ + 90, θ – 90, θ + 180, θ – 180, θ + 270, θ – 270 etc are called allied angles.

According to this, sin (-θ) = -sin θ

                          sin (90 + θ) = sin(90 – θ) = cos θ

                           sin (180 + θ) = -sin θ

        sin(180 – θ) = sin θ

        sin (270 + θ) = sin(270 – θ) = -cos θ