If  $\cos 3\theta -\cos 4\theta =\cos 5\theta -\cos 6\theta$, then  $\theta =$

$\cos 3\theta -\cos 4\theta =\cos 5\theta -\cos 6\theta$

$\cos 3\theta -\cos 5\theta =\cos 4\theta -\cos 6\theta$

$-2\sin 4\theta \sin \theta =-2\sin 5\theta \sin \theta$

$\sin 4\theta .\sin \theta -\sin 5\theta .\sin \theta =0$

$\sin \theta (\sin 4\theta -\sin 5\theta )=0$

$\sin \theta =0.\sin 4\theta -\sin 5\theta =0$

$\sin \theta =0\theta =n\pi .n\in Z$

$\sin 4\theta =\sin 5\theta$

$\cos (90°-4\theta )=\cos (90°-5\theta )$

$90°-4\theta =2n\pi \pm (90°-5\theta )$

$90°-4\theta =2n\pi +90°-5\theta$

$\theta =2n\pi ,n\in Z$

$90°-4\theta =2n\pi -90°+5\theta$

$-9\theta =2n\pi -\pi$

$\theta =(1-2n)\frac{\pi }{9},n\in Z$

$=(2n+1)\frac{\pi }{9},n\in Z$