If tan(θ/2) = 2, then sinθ + cosθ equals:

With $t=2$, sinθ = $2t/(1+t^2)=4/5$ and cosθ = $(1-t^2)/(1+t^2)=(1-4)/5=-3/5$, so the sum is 4/5 − 3/5 = 1/5. The negative cosine is genuine: tan(θ/2) = 2 means θ/2 ≈ 63.43°, so θ ≈ 126.87°, an obtuse angle. Forcing cosθ to be positive gives the trap 7/5.