Consider $=\{\frac{0}{0},\frac{0}{1},\frac{1}{0},\frac{1}{1}\}.$ A string in ${}^{**}$ consists of a top binary string $t$ and a bottom binary string $b$ of equal lengths. For this problem, we regard $t$ and $b$ as numbers expressed in binary notation. Prove that the following language $F$ is regular.

$F=\{w=\frac{t}{b}in{}^{**}|b=3t\}$

Hint: It might be easier to prove that $F^R$ is regular, and use closure.