If ${\mu }_n={\cos }^n\theta +{\sin }^n\theta$  then $2{\mu }_6-3{\mu }_4=$

                                    ${\mu }_4={\sin }^4\theta +{\cos }^4\theta =1-2{\sin }^2\theta .{\cos }^2\theta$

$2{\mu }_6-3{\mu }_4=2\left(1-3{\sin }^2\theta .{\cos }^2\theta \right)-3\left(1-2{\sin }^2\theta .{\cos }^2\theta \right)$

$=2-6{\sin }^2\theta .{\cos }^2\theta -3+6{\sin }^2\theta .{\cos }^2\theta$

$=-1$