Take into account that
cot x = cosx/sinx
use known values of cos300° and sin300° to determine the value of cot300°.
Use equivalents angles, as follow:
cos300° = cos(-60°) = cos60° = 1/2
sin300° = sin(-60°) = -sin60° = -√3/2
then, for cot300°, you obtain:
cot 300° = cos300°/sin300° = (1/2)/(-√3/2) = -2/(2√3) = -1/√3
due to the denominator must be rational, multiply both numerator and denominator of the previous fraction by √3:
(-1/√3)·(√3/√3) = -√3/3
Hence, the exact value of cot300° is -√3/3