Hi George,
usually we upgrade CTA before EOS: you can upgrade CTA and leave your EOS version to 4.8.45.
The reason for this is that we have plenty of eoscta EOS instances and 1 CTA tape backend.
So basically upgrade CTA to the targetted version (we are running cta version 4.6.0) and then look in the CTA CI version lock file which EOS version is coming along with this CTA version.
For version 4.6.0-1 the eos version is 4.8.75 (but you should go straight to 4.8.78).
There is another thread dealing with finding the recommended software matrix: EOSCTA service versions
Julien