Basic probability - either event occurs but not both I'm taking a graduate course in probability and statistics using Larsen and Marx, 4th edition and I'm struggling with a seemingly basic question.

If A and B are any two events, not mutually exclusive: $$P((A \cup B) ^\complement) = 0.6, P(A \cap B) = 0.2$$

What is the probability that A or B occurs, but not both?  Or in other words:  $$P((A \cap B)\ ^\complement \cap (A \cup B)) = ?$$

So far, I've been able to infer the following: $$ P(A \cup B) = 1 - P((A \cup B) ^\complement ) = 1 - 0.6 = 0.4 $$ and $$P((A \cap B) ^\complement) = 1 - P(A \cap B) = 1 - 0.2 = 0.8$$

Can someone kindly give a hint as to how to approach from here?  Am I heading in the right direction?  How should I think about these types of problems in general?  I feel like the text gives you the basic set of axioms to define things but then neglects the showing  of solutions for slightly more complicated examples of compound probability equations such as the above.
Hint: Find the probability of $A$ only plus the probability of $B$ only.

Let $x= P(A~ \text{only})$, $y=P(B ~\text{only})$. Then $x +y + 0.2 =0.4$. Thus $x+y= 0.2$
$P((A \cup B)\setminus(A \cap B)) = P(A\setminus B) + P(A\setminus B) = P(A) + P(B) − 2P(A \cap B)$
  you will get the answer!