Let $\phi(t)$ satisfy the singular integral equation

$$\left(t^{4}+t^{3}-t^{2}\right) \frac{\phi(t)}{2}+\frac{\left(t^{4}-t^{3}-t^{2}\right)}{2 \pi i} \oint_{C} \frac{\phi(\tau)}{\tau-t} d \tau=(A-1) t^{3}+t^{2}$$

where $C$ denotes the circle of radius 2 centred on the origin, $\oint$ denotes the principal value integral and $A$ is a constant. Derive the associated Riemann-Hilbert problem, and compute the canonical solution of the corresponding homogeneous problem.

Find the value of $A$ such that $\phi(t)$ exists, and compute the unique solution $\phi(t)$ if $A$ takes this value.