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The line \( x+2 y=4 \) is translated parallel to itself by 3 units in the sense of increasing \( x \) and then rotated by \( 30^{\circ} \) in the clockwise direction about the point where the shifted line cuts the \( x \)-axis. The equation of the line in the new position, is
(A) \( y=\tan \left(\theta-30^{\circ}\right)(x-4-3 \sqrt{5}) \)
(B) \( y=\tan \left(30^{\circ}-\theta\right)(x-4-3 \sqrt{5}) \)
(C) \( y=\tan \left(\theta+30^{\circ}\right)(x+4+3 \sqrt{5}) \)
(D) \( y=\tan \left(\theta-30^{\circ}\right)(x+4+3 \sqrt{5}) \)
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