Solve the following linear singular equation

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

where $C$ denotes the unit circle, $t \in C$ and $f_{C}$ denotes the principal value integral.