Make Earth invisible to other planets

So, we can see exoplanets but only if they orbit their respective stars at a tilt which casts a shadow away from their star in our angle of perspective.
Wavelengths of light passing through the atmospheres of these worlds can reveal a lot about the gasses comprising these various atmospheres.
Planets not passing in front of their stars are invisible to us aside from gravitational perturbations.

Well...
...that works two ways which means that other planets with the right angle to see us cast our shadow at them can tell we are here and what our atmosphere is comprised of.
If other civilizations are advanced enough to do so, and if expansion and colonization of other worlds is a common trait among species, then we would be pretty ripe pickins.

I propose a colossal undertaking whereby the peoples of Earth endeavour to launch and attach the framework of a gossamer thin series of, planet-and-atmosphere diameter, Fresnel lenses to orbit the world in-line with our star.

The focal distance of these lenses would be such that from our perspective the sun looks just like it did albeit a bit blurry.
From an outside perspective though the light from our star would warp and scatter at angles which could not be detected from any single exo planet previously able to do so.

We would just vanish...

...and then we start on the Dyson sphere!