A majority of photsynthesis on the earth occurs in the oceans, and a majority of that is due to the action of phytoplankton, which inhabit the top few meters of the ocean's water columns.
Phytoplankton blooms, situations where the quantity of phytoplankton increase dramatically, could be engineered
as one way to reduce greenhouse gasses, and possibly forestall other human effects on the environment.
Sadly, the quantity of nutirents needed to feed phytoplankton in these top few meters of the ocean decreases dramatically as one goes away from the shoreline, and out to sea.
Out to sea, the top few meters of the ocean therefore tend to be sparsely populated, and poorly inhabited... until recently... Currently, the top few meters of gyres in the ocean are becoming increasingly populated with human waste. Bits of plastic, which slowly break down into bite sized pieces, thus choking whales, sea birds, and other fish. Not to mention being a general eyesore.
Currently, this plastic is removed from the gyres by one of three ways: Human removal, animal entrapment, and organic encrustation. Human removal is expensive, and if we were ready to do it, there would not be a trash problem in our oceans. Animal entrapment either strangles the animals, or risks blocking the digestive tract of the animal. Neither is desirable. Organic encrustation is caused by organisms such as corals, barnacles, and mussels growing on the floating algae, living a fairly normal life, then dying, and leaving a durable material that is heavier than water on the plastic. The trouble with organic encrustation is that these animals need food, usually in the form of phytoplanktons, which, as I mentioned, are rare in the middle of the ocean.
I propose that the plastic products of our modern society be impregnated with nitrogen, minerals, and other nutrients needed to promote phytoplankton growth. As these bits of plastic drift out to sea, they will slowly break down, and release their nutrients, allowing phytoplankton to grow near them. As these plastics wash out to sea, encrusting species such as barnacles will begin to grow on them, and as there is an abundance of phytoplankton to feed on, these encrusting organisms will thrive. Their shells will then weigh down the bits of plastic, which will sink to the ocean's floor. Phytoplankton growth will increase, cutting down on greenhouse gasses in the atmosphere, and encrusting organisms will leave their shells on the human waste, therby weighing down the plastics so that they sink to the bottom, and are sequestered from further interaction with the environment until a much later date.
Let us now congratulate ourselves on using trash to sequester carbon. We'll worry about what happens to the encrusted trash on the sea floor in another fifty years.