Game freezes upon passing the highest possible value of a double on the Y-axis

Relates to MC-217427.
Like MC-227347, this is private because I am unsure if the reproduction steps are private elsewhere, and I couldn't reproduce this in 1.16.5 for the same reason (kicked before being able to reach this level).

The bug

The game freezes when exceeding the highest possible value of a double on the Y-axis. This number is approximately 1.7976931348623157 x 10^308.

The log is spammed with the following error while experiencing this freeze.

ad     Server thread     Invalid entity rotation: NaN, discarding.

How to reproduce

1. Summon a pig
2. Put a saddle on the pig
3. Ride the pig
4. Put the following command in a command block:

   data merge entity @e[type=pig,sort=nearest,limit=1] {Pos:[0.0,1797693134862315700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.0,0.0]}

5. Activate the command block
   Game freezes, spamming the error above in the log