pbrt v4 book formula 13.9 maybe error

[AndrewChan2022]

simple path trace, direct light evaluate 13.9, P(pi¯) = Le(pi -> pi-1) * f(pi -> pi-1 -> pi-2) * |cosθi| * V(pi <->pi-1) / (pl(wi) * p(l)) * β

here cosθi should be angle on shading surface, so cosθi-1

the code also using shading point angle.

[AndrewChan2022]

formula 14.8,
integrate over majorant segment: third line: miss σ_maj^3

[AndrewChan2022]

text 11.2, delta tracking:

If the Russian roulette termination probability at each sampled point is set to be equal to the ratio of σn and σmaj, then the scaling cancels and the estimator becomes -> termination probability should be 1 - ratio of σn and σmaj

code also using termination probability 1 - σn / σmaj