In advance simplify: (sin θ − cos θ) − (sin θ + cos θ)2 −sin2 θ −cos2 θ 0 −2sin(θ)cos(θ) − cos(θ) + sin(θ) − 1

(sin O - cos O) - (sin O + cos O)^2
= sin O - cos O - (sin^2 O + cos^2 O + 2 sin O cos O)
= sin O - cos  O - ( 1 + 2 sin O cos O)
Distributing the negative over the second set of parentheses:-
= sin O - cos O - 1 - 2 sin O cos O
= -2 sin O cos O - cos O + sin O - 1  (answer)

Its the last choice.