I am doing an assignment and I am being asked to investigate the scaling of the error with the number of repetions $n$ of a approximation of the Hadamard with $R_x$ and $R_y$. This is the approximation, where $\theta = \frac {\pi} {\sqrt2}$: $$ H \equiv \lim_{n\rightarrow\infty} \left( ~R_x\left(\frac{\theta}{n}\right) ~~R_z \left(\frac{\theta}{n}\right) ~\right)^n = e^{i \frac{\theta}2 (X+Z)}$$
I am not sure how to approach this problem. I know that the error $\delta$ is polynomial to $n$ here, but I don't know how to get the scaling more specifically: $$U = \left(e^{i\frac\theta{2n}P}e^{i\frac{\theta}{2n}P'}\right)^n + \delta$$
I appreciate the help!