$\sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}=$

• A

  $1$
• B

  $\sqrt{5}$
• Correct answer
  C

  $\frac{1}{4}(\sqrt{5}+1)(\sqrt{10+2 \sqrt{5}})$
• D

  $\frac{1}{4}(\sqrt{5}-1)(\sqrt{10+2 \sqrt{5}})$

Hence, the correct answer is option: 'C'.