The value of  $3\cos e{c}^2\frac{\pi }{9}-{\sec }^2\frac{\pi }{9}+64{\sin }^2\frac{\pi }{9}=$

$\frac{3}{{\sin }^2{20}^0}-\frac{1}{{\cos }^2{20}^0}+64{\sin }^2{20}^0$ 
$=\frac{6}{1-{\cos }^2{40}^0}-\frac{2}{1+{\cos }^2{40}^0}+32(1-\cos {40}^0)$ 
$=\frac{8\cos {40}^0+4}{1-{\left(\cos {40}^0\right)}^2}+32-32\cos {40}^0$ 
$=\frac{8\cos {40}^0+4-32\cos {40}^0+32{\left(\cos {40}^0\right)}^3}{1-{\left(\cos {40}^0\right)}^2}+32$ 
$=4\times \frac{1-6\cos {40}^0+8{\left(\cos {40}^0\right)}^3}{1-{\left(\cos {40}^0\right)}^2}+32=32$