We will use here those two formulas, sin 2 $\theta$ = ${{1 - \cos 2\theta } \over 2}$ and cos 2 $\theta$ = ${{1 + \cos 2\theta } \over 2}$ L = sin 2 $\left( {{\pi \over {16}}} \right)$ - sin 2 $\left( {{\pi \over {8}}} \right)$ $\Rightarrow$ L = $\left( {{{1 - \cos \left( {{\pi \over 8}} \right)} \over 2}} \right)$ - $\left( {{{1 - \cos \left( {{\pi \over 4}} \right)} \over 2}} \right)$ $\Rightarrow$ L = ${1 \over 2}\left( {\cos \left( {{\pi \over 4}} \right) - \cos \left( {{\pi \over 8}} \right)} \right)$ $\Rightarrow$ L = ${1 \over {2\sqrt 2 }} - {1 \over 2}\cos \left( {{\pi \over 8}} \right)$ M = cos 2 $\left( {{\pi \over {16}}} \right)$ - sin 2 $\left( {{\pi \over {8}}} \right)$ $\Rightarrow$ M = $\left( {{{1 + \cos \left( {{\pi \over 8}} \right)} \over 2}} \right)$ - $\left( {{{1 - \cos \left( {{\pi \over 4}} \right)} \over 2}} \right)$ $\Rightarrow$ M = ${1 \over {2\sqrt 2 }} + {1 \over 2}\cos {\pi \over 8}$