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 want to find the determinant of this Matrix.
$$
\begin{pmatrix}
Tan(A+P) & Tan(B+P) & Tan(C+P)\\
Tan(A+Q) & Tan(B+Q) & Tan(C+Q)\\
Tan(A+R) & Tan(B+R) & Tan(C+R)
\end{pmatrix}
$$
The determinant of this matrix gives us \to
$$
-Tan(A+R) \cdot Tan(B+Q) \cdot Tan(C+P)\\
+Tan(A+Q) \cdot Tan(B+R) \cdot Tan(C+P)\\
+Tan(A+R) \cdot Tan(B+P) \cdot Tan(C+Q)\\
-Tan(A+P) \cdot Tan(B+R) \cdot Tan(C+Q)\\
-Tan(A+Q) \cdot Tan(B+P) \cdot Tan(C+R)\\
+Tan(A+P) \cdot Tan(B+Q) \cdot Tan(C+R)
$$
But I still don't know how to depress it after this, even though you said
$
A+B+C+P+Q+R = 0
$
