Find the general value of `theta`
`sqrt3 cosec theta = 2`

Answer

To solve the equation \( \sqrt{3} \csc \theta = 2 \), we can follow these steps:

### Step 1: Rewrite the equation
The cosecant function is the reciprocal of the sine function, so we can rewrite the equation as:
\[ \sqrt{3} \cdot \frac{1}{\sin \theta} = 2 \]
This simplifies to:
\[ \sqrt{3} = 2 \sin \theta \]

### Step 2: Isolate \(\sin \theta\)
Next, we isolate \(\sin \theta\) by dividing both sides by 2:
\[ \sin \theta = \frac{\sqrt{3}}{2} \]

### Step 3: Find the angles for \(\sin \theta = \frac{\sqrt{3}}{2}\)
The sine function equals \(\frac{\sqrt{3}}{2}\) at specific angles. The primary angles where this occurs are:
\[ \theta = \frac{\pi}{3} \quad \text{and} \quad \theta = \frac{2\pi}{3} \]

### Step 4: Write the general solution
Since the sine function is periodic with a period of \(2\pi\), we can express the general solutions for \(\theta\) as:
\[ \theta = n\pi + (-1)^n \cdot \frac{\pi}{3} \]
where \(n\) is any integer.

### Final Answer
Thus, the general value of \(\theta\) is:
\[ \theta = n\pi + (-1)^n \cdot \frac{\pi}{3}, \quad n \in \mathbb{Z} \]

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