Hints: Property of the predictable variation process

The proof of \((2.10)\) in the book might give some inspiration for this problem. In particular, it is useful to use \[M_n^2 = (M_{n-1}+M_n-M_{n-1})^2\] and from \((2.7)\) that \[\langle M \rangle_n = \langle M \rangle_{n-1} + E[(M_n-M_{n-1})^2|\mathcal{F}_{n-1}].\]