Find $k$, as a function of $d_2$ and $d_3$, such that:
$$\left \vert { d_2 \left [ \sin(e^{d_3\,y}) - \sin(e^{d_3\,x})\right] + (x-y) d_2 d_3 e^{d_3\,z} \cos(e^{d_3\,z})} \right \vert \le k (\vert{x-z}\vert + \vert{y-z}\vert) \,\vert{x-y}\vert$$
Find $k$, as a function of $d_2$ and $d_3$, such that:
$$\left \vert { d_2 \left [ \sin(e^{d_3\,y}) - \sin(e^{d_3\,x})\right] + (x-y) d_2 d_3 e^{d_3\,z} \cos(e^{d_3\,z})} \right \vert \le k (\vert{x-z}\vert + \vert{y-z}\vert) \,\vert{x-y}\vert$$