A particle \(P\) is projected with speed \(u\) at an angle of \(30^{\circ}\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. The particle reaches its greatest height at time \(T\) after projection.

Find, in terms of \(u\), the speed of \(P\) at time \(\frac{2}{3} T\) after projection.