Official solution
\[2\sin 12^\circ - \sin 72^\circ \]
\[ = \sin 12^\circ + ( - 2\cos 42^\circ \,.\,\sin 30^\circ )\]
\[ = \sin 12^\circ - \cos 42^\circ \]
\[ = \sin 12^\circ - \sin 48^\circ \]
\[ = 2\sin 18^\circ \,.\,\cos 30^\circ \]
\[ = - 2\left( {{{\sqrt 5 - 1} \over 4}} \right)\,.\,{{\sqrt 3 } \over 2}\]
\[ = {{\sqrt 3 \left( {1 - \sqrt 5 } \right)} \over 4}\]