This is solvable, but it will require international cooperation on a scale that is unlikely. But you wouldn't need any storage at all, just a large number of long distance HVDC lines to move the energy from wherever the sun is shining to where it isn't.
It solvable but very expensive.
The costs of large number long distance HVDC lines with accompaning invertor stations would be as expensive as a electric generation based on nuclear power.
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