Parametric solutions to $(4/3)b^2c^2+(4/3)a^2d^2-(1/3)a^2c^2-(4/3)b^2d^2=\square$ Let $a,b,c$ and $d$ be rational.Find a rational parametric solutions for $a,b,c$ and $d$ so that 
$$(4/3)b^2c^2+(4/3)a^2d^2-(1/3)a^2c^2-(4/3)b^2d^2=\square.$$

For the equation:
$$4c^2b^2+4d^2a^2-c^2a^2-4d^2b^2=3t^2$$
Can specify any number :  $d,c$ . Then decisions will be.
$$a=(d^2-c^2)p^2+3s^2$$
$$b=(d^2-c^2)p^2-3cps-3s^2$$
$$t=c(d^2-c^2)p^2+4(d^2-c^2)ps-3cs^2$$
$p,s$ - any integer asked us.
