Do you get the free attack from Improved Trip if you make a successful trip attemp on an AOO using Improved Combat Throw?

Improved Combat Throw

Prerequisites: Defensive Martial Arts, Combat Throw, base attack bonus +3.

Benefit: In melee combat, if an opponent attacks and misses the character, the character may immediately make a trip attack against the opponent. This counts as an attack of opportunity, which the character can make even if he or she is unarmed. Attacking unarmed in this way does not provoke an attack of opportunity.

Special: This feat doesn’t grant the character more attacks of opportunity than he or she is normally allowed in a round.

Improved Trip

Prerequisites: Intelligence 13, Combat Expertise.

Benefit: The character does not provoke an attack of opportunity when the character tries to trip an opponent while the character is unarmed.

If the character trips an opponent in melee combat, the character immediately gets to make a melee attack against that opponent as if the character had not used his or her attack action for the trip attempt.