Angle between vectors given its tangent

Consider vectors $\tvec{a} = p\tvec{i} - \tvec{j} + 4\tvec{k}$, $\tvec{b} = -2\tvec{i} + 4\tvec{j} + \tvec{k}$ and $\tvec{c} = -3\tvec{i} - 4\tvec{k}$, where $p$ is a positive integer.

Given $\tan\theta = \sqrt{3}$, where $\theta$ is the angle between $\tvec{a}$ and $\tvec{b} - \tvec{c}$, the value of $p$ is