Suppose instead you were just working with real vectors -- say (2,20,2) and (10,1,1). There is no need to compute the angle between these vectors. There is a much easier way to do this. What is another way to compute the inner product that |a||b|cos(theta)? How would you generalize this to complex numbers?
And finally, what is in your class notes and text? I am quite certain your instructor does not expect you to derive the formula for computing the inner product in C3. He or she expects you to use something you have already been taught.