\(x=A \sin \omega t\)

When displacement

\(x=\frac{A}{2}\)

\(\frac{A}{2}=A \sin (\omega t+\phi)\)

\(\sin ^{-1} \frac{1}{2}=\omega t+\phi\)

\(\omega t+\phi=30^{\circ} \text { or } 150^{\circ}\)

When particles are in opposite direction at one lime phase is \(30^{\circ}\) and at the other \(150^{\circ}\). So phase difference is \(120^{\circ}\).