For `n in Z ,` the general solution of `(sqrt(3)-1)sintheta+(sqrt(3)+1)costheta=2 is(n in Z)` `theta=2npi+-pi/4+pi/(12)` `theta=npi+(-1)^npi/4+pi/(12)` `theta=2npi+-pi/4` `theta=npi+(-1)^npi/4-pi/(12)`

Explanation

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

### Step 1: Normalize the equation
We start by dividing the entire equation by \(2\sqrt{2}\):
\[ \frac{(\sqrt{3}-1)}{2\sqrt{2}}\sin\theta + \frac{(\sqrt{3}+1)}{2\sqrt{2}}\cos\theta = \frac{2}{2\sqrt{2}} \]
This simplifies to:
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