  The long-term evolution of the Sun's rotation period cannot be directly
observed, and is instead inferred from trends in the measured rotation periods
of other Sun-like stars. Assuming the Sun spins-down as it ages, following
rotation rate $\propto$ age$^{-1/2}$, requires the current solar angular
momentum-loss rate to be around $6\times 10^{30}$erg. Magnetohydrodynamic
models, and previous observations of the solar wind (from the Helios and Wind
spacecraft), generally predict a values closer to $1\times 10^{30}$erg or
$3\times 10^{30}$erg, respectively. Recently, the Parker Solar Probe (PSP)
observed tangential solar wind speeds as high as $\sim50$km/s in a localized
region of the inner heliosphere. If such rotational flows were prevalent
throughout the corona, it would imply that the solar wind angular momentum-loss
rate is an order of magnitude larger than all of those previous estimations. In
this letter, we evaluate the angular momentum flux in the solar wind, using
data from the first two orbits of PSP. The solar wind is observed to contain
both large positive (as seen during perihelion), and negative angular momentum
fluxes. We analyse two solar wind streams that were repeatedly traversed by
PSP; the first is a slow wind stream whose average angular momentum flux
fluctuates between positive to negative, and the second is an intermediate
speed stream containing a positive angular momentum flux (more consistent with
a constant flow of angular momentum). When the data from PSP is evaluated
holistically, the average equatorial angular momentum flux implies a global
angular momentum-loss rate of around $2.6-4.2\times 10^{30}$ erg (which is more
consistent with observations from previous spacecraft).
