If `(costheta+cos2theta)^3=cos^3theta+cos^3 2theta,` then the least positive value of `theta` is equal to `pi/6` (b) `pi/4` (c) `pi/3` (d) `pi/2`

Explanation

To solve the equation \((\cos \theta + \cos 2\theta)^3 = \cos^3 \theta + \cos^3 2\theta\), we can start by recognizing that the left-hand side can be expressed using the identity for the sum of cubes.

### Step 1: Rewrite the equation
We know that \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\). Thus, we can rewrite the equation as:
\[ (\cos \theta + \cos 2\theta)^3 = \cos^3 \theta + \cos^3 2\theta \]
This implies:
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