accelerated reference frames equation derivation question

charliepebs

my question comes from the portion of the derivation regarding evaluating the rate of change of the principle axis vectors. this begins by supposing a vector, Q, is rotating about axis n by δθ. Specifically, my question is how from step 4 to step 5 the approximation becomes an equality.

Q' can be approximated as:
1. Q' ≈ Q + (|Q|sinα)δθ(in direction of n cross Q)
2. Q' ≈ Q + |n cross Q|(in direction of n cross Q)δθ
3. Q' ≈ Q + (n cross Q)δθ
4. Q' ≈ Q + δθ cross Q

The derivation then states: "This means that we can express the derivative of this vector as:
5. (Q'-Q)/dt = (δθ cross Q)/dt
6. dQ/dt = δθ/dt cross Q
7. dQ/dt = Ω cross Q