  Stellar streams are particularly sensitive probes of the mass distribution of
galaxies. In this work, we focus on the Helmi Streams, the remnants of an
accreted dwarf galaxy orbiting the inner Milky Way. We examine in depth their
peculiar dynamical properties, and use these to provide tight constraints on
the Galactic potential, and specifically on its dark matter halo in the inner
20 kpc. We extract 6D phase-space information for the Helmi Streams from Gaia
DR3, and confirm that the Streams split up into two clumps in angular momentum
space, and that these depict different degrees of phase-mixing. To explain
these characteristics we explore a range of Galactic potential models with a
triaxial NFW halo, further constrained by rotation curve data. We find that a
Galactic potential with a mildly triaxial dark matter halo, having
$p=1.013^{+0.006}_{-0.006}$, $q=1.204^{+0.032}_{-0.036}$,
$M_{\rm{discs}}=4.65^{+0.47}_{-0.57}\cdot10^{10} M_{\odot}$ and $M_{\rm{DM}}(<
15 \text{kpc})=1.14^{+0.11}_{-0.10}\cdot10^{11} M_{\odot}$, is required to form
two clumps in angular momentum space over time. Their formation is driven by
the fact that the clumps are on different orbital families and close to an
orbital resonance. This resonance also explains the different degrees of mixing
observed, as well as the presence of a dynamically cold subclump (also known as
S2). This first and very precise measurement of the triaxiality of the inner
dark matter halo of the Galaxy uniquely reveals the high sensitivity of
phase-mixed streams to the exact form of the gravitational potential.
