  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, which at the Earth (Sun) can be at least $\simeq 5\times
10^{-3}\,(1)\%$ and $\simeq 1\times 10^{-16}\,(2\times 10^{-14})\%$ for TeV
scale $\gamma$-rays and PeV scale UHE neutrinos respectively. 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.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics;High Energy Physics - Phenomenology