The value of sin(180° + θ)·cos(90° − θ) + cos(180° − θ)·sin(90° + θ) is:

Take the four allied angles one at a time: sin(180° + θ) = −sinθ, cos(90° − θ) = sinθ, cos(180° − θ) = −cosθ and sin(90° + θ) = cosθ. The expression collapses to −si$n^2$θ − co$s^2$θ = −1. Missing both sign flips leaves +1, reading the whole thing as the expansion of sin$(A-B)$ suggests 0, and −2 forgets that si$n^2$θ + co$s^2$θ is already 1.