Let  $f\left(x\right)=\mathrm{sgn}({\sin }^{2}x+2\sin x-3),x\in R$ and $g\left(x\right)=x^2+\left(2m+6\right)x+\left(4m+12\right)$ . If  $g\left(x\right)$ is less than M for at least one real  x  , where $\text{'}M\text{'}$   is maximum value of $f\left(x\right)$  then $\text{'}m\text{'}$  cannot be (sgn=signum function)