如图1，点I是△ABC的内心，AI的延长线交△ABC的外接圆⊙O于点D．

（1）求证：DB=DC=DI；

（2）若AB是⊙O的直径，OI⊥AD，求tan$\frac{\angle CAD}{2}$的值．

    "Haibao, the mascot(吉祥物) of the 2010 Shanghai World Expo, is very cute, "said Gu Hui, a school kid. "I want a big toy like the mascot."

    Haibao looks like the Chinese word ren, which means people or a person. The name, a typical lucky one in Chinese tradition comes from the Chinese phrase "Si Hai Zhi Bao" —the treasure of the four seas. It also means the treasure of Shanghai, which lies beside the sea.

    Haibao's blue curly(卷曲的) hair looks like the waves of the sea. Its smile is a sign of the healthy spirit of China. Those thumbs-up(翘拇指) will welcome millions of people to Shanghai from around the world. Its big feet show China has the ability to host a successful Expo.

    Haibao was created by two artists, one from the mainland(大陆) and the other from Taiwan. The design is about people living together in the city. The designers want it to fit the theme of the Shanghai Expo, that is, a good life should be created by all the people and people should have harmonious relationships(和谐关系) with nature and society, so that life in cities would be better.

    Surely the mascot will become the lucky symbol and cultural remark of Shanghai Expo.

欲测定某石灰石样品中碳酸钙的质量分数（碳酸钙在高温下分解生成氧化钙和二氧化碳；石灰石样品中的杂质受热不分解，且不与酸反应），甲、乙两位同学分别设计了如下两个实验方案：

方案一：①称取石灰石样品质量8g；②用酒精灯加热样品，直至质量不再改变；③将固体残余物放在干燥的器皿中冷却后称得质量6.9 g；④计算。

方案二：①称取石灰石样品质量8 g；②加入质量分数为7.3%的盐酸100 g，使碳酸钙完全反应；③向反应后的溶液中加入含溶质3.2 g的氢氧化钠溶液，恰好中和多余的盐酸；④计算。

请回答下列有关问题：

（1） 碳酸钙在高温下分解的化学方程式是____ ；
（2） 你认为上述方案中，切实可行的是方案____ ，不选用另一方案的原因是____ ；
（3） 求方案二样品中碳酸钙的质量分数____ 。

计算：﹣1²⁰¹⁴﹣6÷（﹣2）×|﹣$\frac{1}{3}$|．