Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than `2/3` of a right angle.

Explanation

To prove that in a triangle, other than an equilateral triangle, the angle opposite the longest side is greater than \( \frac{2}{3} \) of a right angle, we will follow these steps:

### Step 1: Understand the Triangle
Let’s denote the triangle as \( \triangle ABC \) where \( A \), \( B \), and \( C \) are the vertices of the triangle. Assume that \( BC \) is the longest side, which means that angle \( A \) and angle \( C \) are less than angle \( B \).

### Step 2: Establish the Angles
Since \( B \) is the largest angle, we can write:
\[
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