(i) To find the equation of the tangent, we first need the derivative \(\frac{dy}{dx}\) of the curve \(y = \frac{4}{3x-4}\).

The derivative is \(\frac{dy}{dx} = -4(3x-4)^{-2} \times 3\).

Substituting \(x = 2\) into the derivative gives the gradient \(m = -3\).

The equation of the tangent at \(P(2, 2)\) is \(y - 2 = -3(x - 2)\).

(ii) The tangent makes an angle \(\theta\) with the \(x\)-axis, where \(\tan \theta = \pm (-3)\).

This gives \(\theta = \pm 108.4^\circ\) (or \(\pm 71.6^\circ\)).