4 COS2 PI/12 -2

4*cos^2(pi/12)-2?

cos(2x)=2*cos^2(x)-1

2*cos(2x)=4*cos^2(x)-2

therefor, $${\mathtt{4}}{\mathtt{\,\times\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{12}}}}\right)}}^{\,{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}} = {\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{12}}}}\right)} = {\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{6}}}}\right)} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}} = {\sqrt{{\mathtt{3}}}}$$