A particle starts from a point \( \mathrm{z}_{0}=1+\mathrm{i} \), where \( \mathrm{i}=\sqrt{-1} \). It moves horizontally away from origin by 2 units and then vertically away from origin by 3 units to reach a point \( z_{1} \). From \( z_{1} \) particle
\( \mathrm{P} \) moves \( \sqrt{5} \) units in the direction of \( 2 \hat{i}+\hat{j} \) and then it moves through an angle of \( \operatorname{cosec}^{-1} \sqrt{2} \) in
W anticlockwise direction of a circle with centre at origin to reach a point \( z_{2} \). The \( \arg z_{2} \) is given by
(A) \( \sec ^{-1} 2 \)
(B) \( \cot ^{-1} 0 \)
(C) \( \sin ^{-1}\left(\frac{\sqrt{3}-1}{2 \sqrt{2}}\right) \)
(D) \( \cos ^{-1}\left(\frac{-1}{2}\right) \)
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