Yeah, a respondent in the thread (MarGon) pointed that out further down and gave the correct mathematical formula for that constant:
k = 4 * tan(angle / 4). For 90° it will be k = 4 * tan(pi / 8) = 1.6568542494923801
So, the precise value you’re looking for would be 1.6568542494923801… rounded to whatever decimal accuracy you’re going for. (1.65, 1.66, 1.657…)