Prove that `|2alpha+beta+gamma+deltaalphabeta+gammadeltaalpha+beta+gamma+delta2(alpha+beta)(gamma+delta)alphabeta(gamma+delta)+gammadelta(alpha+beta)alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0`

Explanation

To prove that the given determinant is equal to zero, we will follow a systematic approach. Let's denote the determinant as \( D \).

### Step 1: Write the Determinant

The determinant we need to prove is:

\[
D = \begin{vmatrix}
...