The function \(f\) is defined by \(f(x) = 3 \tan\left(\frac{1}{2}x\right) - 2\), for \(-\frac{1}{2}\pi \leq x \leq \frac{1}{2}\pi\).

(i) Solve the equation \(f(x) + 4 = 0\), giving your answer correct to 1 decimal place. [3]

(ii) Find an expression for \(f^{-1}(x)\) and find the domain of \(f^{-1}\). [5]

(iii) Sketch, on the same diagram, the graphs of \(y = f(x)\) and \(y = f^{-1}(x)\). [3]