`tan^6(pi/9)-33tan^4(pi/9)+27tan^2(pi/9)` is equal to (a)0 (b) `sqrt3` (c) 3(d)9

Explanation

To solve the expression \( \tan^6\left(\frac{\pi}{9}\right) - 33\tan^4\left(\frac{\pi}{9}\right) + 27\tan^2\left(\frac{\pi}{9}\right) \), we can follow these steps:

### Step 1: Let \( x = \tan^2\left(\frac{\pi}{9}\right) \)
We can rewrite the expression in terms of \( x \):
\[ x^3 - 33x^2 + 27x \]

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