A linear Algebra Problem (3x3 Matrix)

[timelyrainsun]

Homework Statement

I want to proove the determinant of the following 3x3 matrix is 0.

1 1 1

tanA tanB tanC

tan2A tan2B tan2C

where A+B+C=2pi.

Homework Equations

Sorry I don't know how to type here so I show in the attachment.

The Attempt at a Solution

Sorry I have attempted but found no way closed to the solution.

 

[HallsofIvy]

If you want to do it then you first have to attempt to do it and you have shown no attempt. Under "relevant equations" you might put something like
$$\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|= a\left|\begin{array}{cc}e & f \\ h & i\end{array}\right|- b\left|\begin{array}{cc}d & f \\ g & i\end{array}\right|+ c\left|\begin{array}{cc}d & e \\ g & h\end{array}\right|$$
as well as some trig identities like
$$tan(2A)= \frac{2tan(A)}{1+ tan^2(A)}$$

 

[timelyrainsun]

f

If you want to do it then you first have to attempt to do it and you have shown no attempt. Under "relevant equations" you might put something like
$$\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|= a\left|\begin{array}{cc}e & f \\ h & i\end{array}\right|- b\left|\begin{array}{cc}d & f \\ g & i\end{array}\right|+ c\left|\begin{array}{cc}d & e \\ g & h\end{array}\right|$$
as well as some trig identities like
$$tan(2A)= \frac{2tan(A)}{1+ tan^2(A)}$$

Sorry it is my bad. Thanks!