## Math Problem Statement

Suppose that π΄, π΅, πΆ are the three interior angles of an acute-angled triangle, that is, π΄ + π΅ + πΆ = 180Β° and 0Β° < π΄, π΅, πΆ < 90Β°. given that tan π΄ + tan π΅ + tan πΆ = tan π΄ tan π΅ tan πΆ. (a) By using the equation given and the AM-GM inequality, find the minimum value of π = tan π΄ tan π΅ tan πΆ and determine the values of π΄, π΅, πΆ at which the minimum value of π is attained

## Solution

## Math Problem Analysis

### Mathematical Concepts

Trigonometry

AM-GM Inequality

Triangle Geometry

### Formulas

\( A + B + C = 180^\circ \)

\( \tan A + \tan B + \tan C = \tan A \tan B \tan C \)

### Theorems

AM-GM Inequality

### Suitable Grade Level

Advanced High School

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