Trig

The angle sum formula should work:

$\sin {(\frac{2\pi}{15})}\cos {(\frac{4\pi}{5})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{4\pi}{5})}\\ =\sin {(\frac{2\pi}{15})}\cos {(\frac{12\pi}{15})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{12\pi}{15})}\\ =\sin {(\frac{-10\pi}{15})}\\ =\sin{\frac{-2\pi}{3}}\\ = -\frac{\sqrt 3}{2}$