I was referring to using cosine in Newton's law. This:
$$ \sum F = - T_{B} - mgcos(\phi)$$
Should be:
$$ \sum F = - T_{B} - mgsin(\phi)$$
It is the component of the weight parallel to the plane that contributes to the radial acceleration and not the perpendicular component, i.e the normal.
I am not sure how did you get the component of the weight in the radial direction towards the center at point b to involve a cosine. It should be a sine instead. That would obviously change the final solution but other than that everything else is good.