What is the value of \cos (\frac{5 \pi}{17})+\cos (\frac{7 \pi}{17})+ 2 \cos (\frac{11 \pi}{17}) \cos (\frac{\pi}{17}) ? [NDA II 2022]

4 \cos (\frac{6 \pi}{17}) \cos (\frac{\pi}{17})

4 \cos (\frac{11 \pi}{17}) \cos (\frac{\pi}{17})