If $\sin \alpha = \frac{1}{\sqrt{2}}$ and $\cot \beta = \sqrt{3}$, then find the value of $\cosec \alpha + \cosec \beta$.

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Step 1: $\cosec \alpha = \frac{1}{\sin \alpha} = \sqrt{2}$
Step 2: $\cosec \beta = \sqrt{1 + \cot^2 \beta} = \sqrt{1 + 3} = 2$
Step 3: $	herefore \cosec \alpha + \cosec \beta = \sqrt{2} + 2$ or $\sqrt{2}(\sqrt{2} + 1)$

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