Both answers are not the same. You are correct and your friend is wrong. The situation your teacher gave could have only one other interpretation that would be acceptable and that would be 8t+3 because it is the same number just in a different order.
tan( tehta ) = 2/3
Sin( tetha ) = 2/√13
tan( tetha ) + Sin( tetha ) = 2/3 + 2/√13
= 2√13 + 6 / 3√13
