the asymptote of function cot (n) basically is located at zeros of tan (n) where n = m*pi and m is any positive or negative integer. therefore, asymptotes of 2 cot(x/3) is at x = 3m*pi for m = 0. -1, 1, ....to locate two asymptotes we late m=0 and m= 1. in this case x = 0 and x= 3*pi

then, our first asymptote will be 2cot(0) and the second will be 2cot(3*pi)