If `cos^(-1)lambdacos^(-1)mu+cos^(-1)gamma=3pi,` then find the value of `lambdamu+mulambdadot`

Explanation

To solve the equation \( \cos^{-1}(\lambda) + \cos^{-1}(\mu) + \cos^{-1}(\gamma) = 3\pi \), we can follow these steps:

### Step 1: Understand the Range of Inverse Cosine
The function \( \cos^{-1}(x) \) has a range of \( [0, \pi] \). Therefore, for the sum of three inverse cosine functions to equal \( 3\pi \), each individual term must be at its maximum value of \( \pi \).

### Step 2: Set Each Inverse Cosine to Its Maximum Value
Since \( \cos^{-1}(\lambda) + \cos^{-1}(\mu) + \cos^{-1}(\gamma) = 3\pi \), we can conclude:
\[
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