The curves $\displaystyle \vec{{r}}_{{1}}{\left({t}\right)}={\left\langle-{t},{t}^{{{5}}},{5}{t}^{{{2}}}\right\rangle}$ and $\displaystyle \vec{{r}}_{{2}}{\left({t}\right)}={\left\langle{\sin{{\left(-{3}{t}\right)}}},{\sin{{\left(-{4}{t}\right)}}},{t}-\pi\right\rangle}$ intersect at the origin.

Find the acute angle of intersection (in radians) on the domain $\displaystyle {0}\le{t}\le\pi$, to at least two decimal places.