  The Sun emits copious amounts of photons and neutrinos in an approximately
spatially isotropic distribution. Diffuse $\gamma$-rays and ultra-high energy
(UHE) neutrinos from extragalactic sources may subsequently interact and
annihilate with the emitted solar photons and neutrinos respectively. This will
in turn induce an anisotropy in the cosmic ray (CR) background due to
attenuation of the $\gamma$-ray and UHE neutrino flux by the solar radiation.
Measuring this reduction, therefore, presents a simple and powerful
astrophysical probe of electroweak interactions. In this letter we compute such
anisotropies for TeV $\gamma$-rays, which at the Earth (Sun) can be at least
$\simeq 10^{-4},(10^{-2})$. The optical depth at Earth for elongation angles
more focused around the Sun ($\lesssim 10^\circ$), can be around $10^{-3}$ and
larger. Neutrino attenuation is extremely tiny for for PeV scale UHE neutrinos.
We briefly discuss observational prospects for experiments such as the Fermi
Gamma-Ray Space Telescope Large Area Telescope (Fermi LAT), High-Altitude Water
Cherenkov (HAWC) detector, The Large High Altitude Air Shower Observatory
(LHAASO), Cherenkov Telescope Array (CTA) and IceCube. The potential for
measuring $\gamma$-ray attenuation at orbital locations of other active
satellites such as the Parker Solar Probe and James Webb Space Telescope (JWST)
is also explored.
