$VT=\Big(\sin\dfrac{\pi}{24}.\sin\dfrac{11\pi}{24}\Big).\Big(\sin\dfrac{5\pi}{24}.\sin\dfrac{7\pi}{24}\Big)$
$=-\dfrac{1}{2}\Big(\cos\dfrac{\pi}{2}-\cos\dfrac{5\pi}{12}\Big).\dfrac{-1}{2}.\Big(\cos\dfrac{\pi}{2}-\cos\dfrac{\pi}{12}\Big)$
$=\dfrac{1}{4}.(-1).(-1).\cos\dfrac{5\pi}{12}.\cos\dfrac{\pi}{12}$
$=\dfrac{1}{4}.\dfrac{1}{2}\Big(\cos\dfrac{\pi}{2}+\cos\dfrac{\pi}{3}\Big)$
$=\dfrac{1}{4}.\dfrac{1}{2}.\dfrac{1}{2}$
$=\dfrac{1}{16}$
$=VP$