If `(tanx)/2=(tany)/3=(tanz)/5,x+y+z=pi` and `tan^2x+tan^2y+tan^2z` is

Explanation

To solve the problem, we need to find the value of \( \tan^2 x + \tan^2 y + \tan^2 z \) given that \( \frac{\tan x}{2} = \frac{\tan y}{3} = \frac{\tan z}{5} \) and \( x + y + z = \pi \).

### Step-by-step Solution:

1. **Set up the equations**:
Let \( k = \frac{\tan x}{2} = \frac{\tan y}{3} = \frac{\tan z}{5} \). This gives us:
\[
\tan x = 2k, \quad \tan y = 3k, \quad \tan z = 5k
...