The functions \(\mathrm f\) and \(\mathrm g\) are defined as follows, for all real values of \(x\).

\(\mathrm f:x\mapsto2\sin x+3\cos x\)

\(\mathrm g:x\mapsto \mathrm e^{3x}-1\)

(a) Find the value of \(\mathrm{fg}(0)\).

(b) Find \(\mathrm{gg}(x)\) in terms of \(x\), giving your answer in its simplest form.

(c) Solve the equation \(\mathrm g^{-1}(x)=\frac13\ln5\).