RTP: \left|\dfrac{15 + 12\cos{\theta}}{16\sin{\theta}\cos{\theta}+20\sin{\theta}}\right| = \left|\dfrac{15 - 12\cos{\theta}}{16\sin{\theta}\cos{\theta}-20\sin{\theta}}\right|
LHS = \dfrac{3}{4\left|\sin{\theta}\right|}\left|\dfrac{5 + 4\cos{\theta}}{4\cos{\theta}+5}\right|
LHS = \dfrac{3}{4\left|\sin{\theta}\right|}
RHS = \dfrac{3}{4\left|\sin{\theta}\right|}\left|\dfrac{5 - 4\cos{\theta}}{4\cos{\theta}-5}\right|
RHS = \dfrac{3}{4\left|\sin{\theta}\right|}\left|\dfrac{5 - 4\cos{\theta}}{-(-4\cos{\theta}+5)}\right|
RHS = \dfrac{3}{4\left|\sin{\theta}\right|}\left|-1\right|
RHS = \dfrac{3}{4\left|\sin{\theta}\right|} = LHS
Q.E.D
