Given $A+B+C=180^{\circ}$, find value of $\tan A\cdot\tan B+\tan B\cdot\tan C+\tan A\cdot \tan C-\sec A\cdot\sec B\cdot\sec C$ 
Given $A+B+C=180^{\circ}$, find value of $$\tan A\cdot\tan B+\tan B\cdot\tan C+\tan A\cdot \tan C-\sec A\cdot\sec B\cdot\sec C$$

I know about some basic conditional identities but don't know how to use them here.

$$\dfrac{\sin A\sin B\cos C+\sin B\sin C\cos A+\sin C\sin A\cos B-1}{\cos A\cos B\cos C}$$
As $C+A=\pi-B,\sin(C+A)=\sin B,\cos(C+A)=-\cos B$
Now,$\sin A\sin B\cos C+\sin B\sin C\cos A$
$=\sin B\sin(C+A)=\sin^2B=1-\cos^2B=1+\cos B\cos(C+A)$
$\sin A\sin B\cos C+\sin B\sin C\cos A+\sin C\sin A\cos B$
$=1+\cos B\cos(C+A)+\sin C\sin A\cos B$
$=1+\cos B\{\cos(C+A)+\sin C\sin A\}$
$=1+\cos B(\cos C\cos A-\sin C\sin A+\sin C\sin A)$
$=1+\cos A\cos B\cos C$
Can you take it from here?
