Java.util.date get the actual date at client timezone

Searching up and down, right and left - don't find simple answer to this question:

I have java.util.Date instance, which get its value from mySQL.

Also I have time-zone code of the logged-in user.

I need to get the actual time at user time-zone.

For example:

My server-machine time-zone is GMT+2.

My date value in DB is: 2017-02-09 16:38:58.000

According to my server-machine-time-zone I get it into date instance as: 2017-02-09T16:38:58.000+0200

Now I need to know what to do if:

In case, for sample, my client-time-zone-code is GMT+4, I want to get:

2017-02-09 20:38:58.000

Pure date, that is right to my time zone and not contain "+4" or "GMT" indication.

In short words: convert my java.util.date to pure date that right to specific time-zone.

Sound very simple? after read very much documentaion, I already not sure that this is really simple.