Periodic Function

Q. Which of the following is/are correct?

1. The number of real solution of $2^{x^2}\sec x=1$ is $1$.
2. The number of real ordered point $(x,y)$ satisfying the system of equations $6^x{\left(\frac{2}{3}\right)}^y-3\cdot 2^{x+y}-8\cdot 3^{x-y}+24=0$ and $xy=2$ is $2$
3. The number of real solution of ${\log }_2(4\cdot 3^x-6)-{\log }_2(9^x-6)=1$ is $1$
4. $\tan \left(\frac{\pi }{8}\right)+\cot \left(\frac{\pi }{8}\right)=2\sqrt{2}$

Q. Let the function $f\left(x\right)$ and $g\left(x\right)$ be defined as
$f\left(x\right)=\{\begin{array}{cc}\sqrt{x}& 0\le x<1\\ 2-x& 1\le x<2\\ f(x+2)& \forall x\in R\end{array}$ and $g\left(x\right)=4f\left(3x\right)+1,\forall x\in R$.

Let $A$ denotes the sum of all the solutions of the equation $f\left(x\right)=0.6,3\le x\le 7$.
$B$ denotes the fundamental period of $g\left(x\right)$.
$C$ denotes the value of $g^{\prime }\left(6.75\right)$.
Then, the value of $\left[ABC\right]$ is
(where [.] represents greatest integer function)