How to make cyclohex-4-ene-1,2-diol from cyclohexa-1,4-diene?
I think the easier way of doing this is to epoxidise the diene with 1 eq of a peracid epoxidation with peracids . The standard reagent m-Chloroperoxybenzoic acid (MCPBA) breaks your rule of organic molecules with 3 carbon atoms or fewer, but you can also do it with peracetic or pertrifluoroacetic acid preparation of peracetic acid. You will inevitably get some di-epoxide, but this will be separable by chromatography. The mono-epoxide can then be reacted in mild aqueous acid to give the diol. You could also carry the mixture through to the aqueous acid treatment as the tetraol will be far more water soluble than the diol and can be removed by an aqueous wash.