What is the reference angle for ##(14pi)/3##?

It is always possible to add, or subtract, ##2pi## to an angle to obtain an equivalent one. The symbol ##-=## in the following passages is not a real ##=##, but only an equivalent symbol.

##14/3pi-2pi -= 8/3pi -= 8/3pi-2pi -= 2/3pi##.

##2/3pi## is just ##pi/3## less that ##pi## so the acute angle (the reference angle) between ##2/3 pi## and the horizontal is ##pi/3##

Because they are coterminal, the reference angle for ##14/3pi## is the same. It is ##pi/3##.