Star Alliance member airline LOT Polish launches service between LAX and Warsaw in April 2017. There are low fares from $548 to $648 for flights to southeastern Europe and Moscow in April and May, then September to December.,
Many of these itineraries force overnight layover in Warsaw. Airport transportation into Warsaw is inexpensive and hotels are cheap too, so not too bad a stopover.
LAX-Belgrade $652 (also available Christmas season).