Given a regular curve $\Gamma_1$ whose natural parametric equation is that $$\Gamma_1:\quad \begin{cases} \displaystyle x=\frac{s}{2}-\sin\frac{s}{2}\\ \displaystyle y=1-\cos\frac{s}{2}\\ \displaystyle z=4\sin\frac{s}{4}\\ \end{cases}$$ How to find a regular curve $\Gamma_2$ such that $(\Gamma_1,\Gamma_2)$ become Bertrand pair of curves?
Where the fixed angle between two tangent vectors to these two curves is $\frac{\pi}{3}$ at each corresponding point.
Note: In case you're not familiar with these topics, you'll find links to more information in the Reference of this post.
Reference: https://en.wikipedia.org/wiki/Differential_geometry_of_curves