Find the value of p for which the function $f(x)=\left\{\begin{array}{ 1 1}\large\frac{(4^x-1)^3}{\sin\big(x/p\big)\log \big(1+\Large\frac{x^2}{3}\big)}&x\neq 0\\12(\log 4)^3&x=0\end{array}\right.$ is continuous at $x=0$

Question

$(a)\;1\qquad(b)\;4\qquad(c)\;3\qquad(d)\;2$