It means that yes, the big powers did give Cyprus its independence, symbolically, but effectively, its government was still dependent on Greece, Turkey and Britain.
dependance was of quaranteeing the integrity and upholding the constitution and thats all.. nothing about ethnic cleansing and colonization. this is a fact which is documented. and i bet kifeas will be able to give you more on the invasion as the RoC was a member of the un charter.
anyway, i think if you concetrate on specific issues as the akritas plan you will do better rather than concetrate on the inter communal fighting.
also the tcs had their own version. worth looking into this as well.