If cosθ − sinθ = √2·sinθ, then cosθ + sinθ equals:

Collect the sines: cosθ = (√2 + 1)sinθ. Then cosθ + sinθ = (√2 + 1)sinθ + sinθ = (√2 + 2)sinθ = √2(√2 + 1)sinθ = √2·cosθ. The angle is θ = 22.5°: 0.9239 + 0.3827 = 1.3066 and √$2\times 0.9239=1.3066$. Simply copying the √2 onto the same ratio gives the trap √2·sinθ.