Converting RTC gamma0 to sigma0

There are several posts on this topic, but none seem to explicitly answer my present confusion.

There is ellipsoid-based gamma0 and terrain-flattened gamma0, and it seems that they are often given with the same symbology despite being different.

ASF provides ALOS/PALSAR RTC data products in gamma0 (correction procedure here). These RTC data include incidence angle maps (I think its the local incidence angle from the DEM used for terrain correction). What equation can I use to convert these RTC gamma0 values to RTC sigma0 based on the local incidence angle?

For gamma0 calibrated using the incidence angle relative to the Earth ellipsoid, it seems that sigma0 = gamma0 * cos(θ) based on the relationship of the areas used for normalization when converting from beta0 to gamma0 and sigma0 (e.g., Small 2011).

However, in the 2D diagram below (from TerraSAR-X guide) where θ is the local incidence angle and backscatter coefficients are represented as sides of a triangle, the geometry is such that sigma0 = gamma0 / cos(θ).

So, using the local incidence angle for RTC data, is it:
(1) sigma0 = gamma0 * cos(θ)
(2) sigma0 = gamma0 / cos(θ)
Or perhaps something more involved? It seems to depend on whether or not you’re using the local incidence angle and whether or not the backscatter coefficients are already terrain-corrected, but I’m not confident what is appropriate for my case.

Thanks for any help.