Problem:
We are given the trigonometric expression:
\[
\sin^2\theta + \sin\theta + \cos^2\theta
\]
We are to find the value of \( \theta \) for which the expression equals 2.
Step 1: Use trigonometric identity
Recall the fundamental identity:
\[
\sin^2\theta + \cos^2\theta = 1
\]
So we substitute this into the given expression:
\[
\sin^2\theta + \cos^2\theta + \sin\theta = 1 + \sin\theta
\]
Step 2: Set the expression equal to 2
\[
1 + \sin\theta = 2
\Rightarrow \sin\theta = 2 - 1 = 1
\]
Step 3: Solve for \( \theta \)
\[
\sin\theta = 1
\Rightarrow \theta = 90^\circ \quad \text{(or in radians: } \frac{\pi}{2} \text{)}
\]
This is because sine of 90° is exactly 1.
Final Answer:
The required value of \( \theta \) is \(90^\circ\) or \(\frac{\pi}{2}\) radians.