Sorry for your loss OP.
I think he raised a very valid point, google phone number of Coinbase will come back a fake one. And the fake one will steal your coin.
This.
Don't use Google!
The ads a the top tend to be phishing sites, and in the search results they tend to also list scam sites. You are safer bookmarking login urls, rather than googling and automatically clicking what is at the top (which is sometimes the site you want and sometimes a phoshing ad).
Coinbase is also at fault - they should have listed their phone number on their website, so OP didn't have to google.
But if they actually listed their number in a reasonable, easy to find place, people might actually call it, *gasp*

(Google is notorious for this btw themselves; try to actually reach a human at Google Adwords. There is a number, yes, but its bullshit. It takes you to what is essentially a machine reading off the same help article you just read before you picked up the phone
This was a social engineering attack, you got out clevered. I had to reread the OP a few times to understand what went down there, and a few of the comments. All the anitvirus, air gaps and armed guards can't stop shit like this. I think they were able to access your account because they had your credentials, as you thought it was a legit support rep you were talking too). Be smart; if you ever have suspect login issues, contact support via email immediately. Email is free, and they will lock your account or be liable themselves. Its a pain to unlock when you have to do this (you will have to submit veri info), but the alternative is sooo much worse