To determine the dihedral angle of the least stable conformer of ethane, we need to understand the concept of conformational isomerism in alkanes.$\\$Ethane ($$C$_2$H$_6$) can exist in different conformations due to rotation around the carbon-carbon single bond. The two primary conformations are:$\\$• Staggered conformation: where the hydrogen atoms on adjacent carbons are as far apart as possible.$\\$• Eclipsed conformation: where the hydrogen atoms on adjacent carbons are aligned with each other.$\\$The dihedral angle is the angle between the planes formed by the bonds on adjacent carbons.$\\$In the staggered conformation, the dihedral angle is $60^{\circ}$, which is the most stable conformation due to minimal torsional strain.$\\$In the eclipsed conformation, the dihedral angle is $0^{\circ}$, which is the least stable conformation due to maximum torsional strain.$\\$Therefore, the dihedral angle of the least stable conformer of ethane is $0^{\circ}. \\$This corresponds to Option 4.