$cos \theta = l_1l_2 + m_1m_2 + n_1n_2$
$\begin{array}{l}\cos \,\,\theta \,\, = \,\,\left( {\frac{{\sqrt 3 }}{4}} \right)\,\,\left( {\frac{{\sqrt 3 }}{4}} \right)\,\, + \;\,\left( {\frac{1}{4}} \right)\,\,\left( {\frac{1}{4}} \right)\,\, + \;\,\left( {\frac{{\sqrt 3 }}{2}} \right)\,\,\left( { - \frac{{\sqrt 3 }}{2}} \right)\\\cos \,\,\theta \,\, = \,\,\frac{3}{{16}}\,\, + \;\,\frac{1}{{16}}\,\, - \,\,\frac{3}{4}\,\, = \,\,\frac{{3\,\, + \;\,1\,\, - \,\,12}}{{16}}\,\, = \, - \frac{8}{{16}}\,\, = \,\, - \frac{1}{2}\,\,\therefore \,\,\theta \,\, = \,\,120^\circ \end{array}$
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