Finding value of determinant, Where $A+B+C+P+Q+R=0$ Finding value of Determinant $$\begin{vmatrix}
\tan (A+P) & \tan(B+P)  & \tan(C+P)\\\\ 
 \tan (A+Q)& \tan (B+Q)  & \tan (C+Q)\\\\ 
 \tan (A+R)&\tan (B+R)  & \tan(C+R) 
\end{vmatrix}$$ for all values of $A,B,C,P,Q,R$ Where $A+B+C+P+Q+R=0$
I did not understand how to start it, Could some help me, Thanks

We have that if $X+Y+Z = 0$, then $\tan X+ \tan Y+\tan Z = \tan X \tan Y \tan Z$.
Hence for example $$\tan (A+P) \tan (B+Q) \tan (C+R) = \tan (A+P) +\tan (B+Q) +\tan (C+R)$$
Hence when you expand from R1, the determinant expands as 
$$\begin{align} & \left(\tan (B+Q) +\tan (C+R)-\tan (C+Q) - \tan (C+R)\right)\\
+ & \left(\tan (C+Q)+\tan (A+R) - \tan (A+Q)-\tan (C+R)\right)\\
+ & \left(\tan (A+Q)+\tan (B+R) - \tan (A+R) - \tan (B+Q)\right)\end{align} = 0$$
