The mechanism would be addition of halogens. Since it is in non-polar solvent, two chlorines with attached across each the double bond.
Work Step by Step
Since there are two double bonds and two moles of $Cl_2$, the reaction with happen at both the double bonds. The chlorines will be added trans. The mechanism would be: 1) Electrophilic attack forms a chloronium ion. 2) The chloride ion opens the chloronium ion. All stereoisomers will be produced considering that the chlorines attached to the double bond are always trans.