State true or false for the following : The argument of the complex number $\;z=(1+ i\sqrt{3})(1+i)(cos \theta + i sin \theta)\;$ is $\; \large\frac{7 \pi}{12} + \theta$

$(a)\;True\qquad(b)\;false$

Explanation :
True , because
$\;arg(z)=arg(1+ i\sqrt{3})+ arg(1+i) +arg(cos \theta + i sin \theta)\;$
$\large\frac{\pi}{3}+ \large\frac{\pi}{4} + \theta = \; \large\frac{7 \pi}{12} + \theta$