Expectation of quadratic variation

Question

I got stuck in a step of a proof and need some help. The situation is the following: Let $M$ be a continuous local martingale (which satisfies $\mathbb{E}[\langle M\rangle(T)]<\infty$ - I don't think that this particular fact is important for the following question) and $\tau_k$ be a localizing sequence of stopping times for $M$ AND $M^2-\langle M\rangle$. The claim now is that $\mathbb{E}[M(\tau_k)^2]=\mathbb{E}[\langle M\rangle(\tau_k)]$. Why is this true? Thanks a lot in advance!