>>16806422

vertices H, K, and L are collinear
<==>
Det[{{s + t – 2 + s*cos(π + θ + π/2), 1 + s*sin(π + θ + π/2), 1}, {2 – s – t + √2*s*cos(θ + π/4), √2*s*sin(θ + π/4) – 1, 1}, {2 – s – t + s*cos(θ + π/2), s*sin(θ + π/2) – 1, 1}}] = 0
<==>
(2 – s – t)*sin(θ) + cos(θ) = s