已知：$\overrightarrow{a}$、$\overrightarrow{b}$、$\overrightarrow{c}$是同一平面上的三个向量，其中$\overrightarrow{a}$=（1，2）．

（1）若|$\overrightarrow{c}$|=2$\sqrt{5}$，且$\overrightarrow{c}$∥$\overrightarrow{a}$，求$\overrightarrow{c}$的坐标．

（2）若|$\overrightarrow{b}$|=$\frac{\sqrt{5}}{2}$，且$\overrightarrow{a}$+2$\overrightarrow{b}$与2$\overrightarrow{a}$﹣$\overrightarrow{b}$垂直，求$\overrightarrow{a}$与$\overrightarrow{b}$的夹角θ

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