  The one-loop corrections to the weak mixing angle $\sin^2\theta_{eff}^b$
derived from the $Z{\bar b}b$ vertex, are known since 1985. It took another 30
years to calculate the complete electroweak two-loop corrections to
$\sin^2\theta_{eff}^b$. The main obstacle was the calculation of the O(700)
bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$.
We did not perform the usual integral reduction and master evaluation, but
chose a completely numerical approach, using two different calculational
chains. One method relies on publicly available sector decomposition
implementations. Further, we derived Mellin-Barnes (MB) representations,
exploring the publicly available MB suite. We had to supplement the MB suite by
two new packages: AMBRE~3, a Mathematica program, for the efficient treatment
of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian
space-time. Our preliminary result for LL2016, the "dessert", for the
electroweak bosonic two-loop contributions to $\sin^2\theta_{eff}^b$ is:
$\Delta \sin^2\theta_{eff}^{b(\alpha^2,\rm bos)} = \sin^2\theta_W ~
\Delta\kappa_b^{(\alpha^2,bos)}$, with $\Delta\kappa_b^{(\alpha^2,bos)} =
-1.0276 x 10^{-4}$. This contribution is about a quarter of the corresponding
fermionic corrections and of about the same magnitude as several of the known
higher-order QCD corrections. The $\sin^2\theta_{eff}^b$ is now predicited in
the Standard Model with a relative error of $10^{-4}$ [1].
