A particle \(P\) is projected with speed \(u \mathrm{~m} \mathrm{~s}^{-1}\) at an angle of \(\theta\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. The horizontal and vertical displacements of \(P\) from \(O\) at a subsequent time \(t \mathrm{~s}\) are denoted by \(x \mathrm{~m}\) and \(y \mathrm{~m}\) respectively.
(a) Show that the equation of the trajectory is given by
\(y=x \tan \theta-\frac{g x^{2}}{2 u^{2}}\left(1+\tan ^{2} \theta\right) .\)

In the subsequent motion \(P\) passes through the point with coordinates \((30,20)\).
(b) Given that one possible value of \(\tan \theta\) is \(\frac{4}{3}\), find the other possible value of \(\tan \theta\).