(12) - Outcoming - A problem redone.

$\text{ABC}$ is an obtuse triangle such that

$\large \begin{cases} \dfrac{3\text{BC} - \text{AB}}{4\text{BC}} = \sin^2\text{A} \\ \dfrac{1}{2}\cot\dfrac{\text{A}}{2} = \sin\text{A} + \sin\text{B} + \sin\text{C}\\ \cos^2\text{A} + \cos^2\text{B} + \cos^2\text{C} = p \end{cases}$

Calculate the value of $p$ .