Log2 (sin pi/8) + log2 (2cos pi/8)

[latex]\log_2(\sin\frac{\pi}{8})+\log_2(2\cos\frac{\pi}{8})=\log_2(2\cos\frac{\pi}{8}\sin\frac{\pi}{8})=\log_2(\sin(2\frac{\pi}{8}))=[/latex] [latex]=\log_2(\sin\frac{\pi}{4})=\log_2( \frac{\sqrt{2}}{2} )=\log_2( \frac{1}{\sqrt{2} } )=\log_2(2^{-\frac{1}{2}} )=-\frac{1}{2} [/latex]