To solve this expression, we first need to determine the values of arctan(1/3) and arccot(-√3).

Calculate arctan(1/3):
tan(arctan(1/3)) = 1/3
Therefore, arctan(1/3) = tan^(-1)(1/3)

Calculate arccot(-√3):
cot(arccot(-√3)) = -√3
Therefore, arccot(-√3) = cot^(-1)(-√3)

Now, we can substitute these values back into the original expression:

arctan(1/3) + arccot(-√3) = tan^(-1)(1/3) + cot^(-1)(-√3)

Since tan^(-1)(1/3) + cot^(-1)(-√3) are not directly computable, we cannot simplify this expression further.