Find the value of ` ^4nC_0+^(4n)C_4+^(4n)C_8++""^(4n)C_(4n)` .

Explanation

To find the value of \( \binom{4n}{0} + \binom{4n}{4} + \binom{4n}{8} + \ldots + \binom{4n}{4n} \), we can use the Binomial Theorem and some properties of binomial coefficients.

### Step 1: Understanding the Sum
We need to find the sum of the binomial coefficients where the indices are multiples of 4. This can be expressed in terms of powers of complex numbers using the Binomial Theorem.

### Step 2: Using Binomial Theorem
The Binomial Theorem states that:
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