The smallest positive angle which satisfies the equation `2sin^2theta+sqrt(3)costheta+1=0` is `(5pi)/6` b. `(2pi)/3` c. `pi/3` d. `pi/6`

Explanation

To solve the equation \(2\sin^2\theta + \sqrt{3}\cos\theta + 1 = 0\), we will follow these steps:

### Step 1: Rewrite the equation using the Pythagorean identity
We know that \(\sin^2\theta = 1 - \cos^2\theta\). Substituting this into the equation gives:
\[ 2(1 - \cos^2\theta) + \sqrt{3}\cos\theta + 1 = 0 \]
This simplifies to:
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