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Solve a complicated simultaneous equation with the trigonometric terms?

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Hi, everyone. I'm new about this tool. I want to solve a simultaneous equation with the trigonometric terms which is really complicated for me. I'm not sure whether the way I operate the tool is right. Until today the time of calculation is about 7 hours. Is there any advice to solve this problem or is there any problem with my operation? The code is shown below and the file is attached. Thanks a lot!!

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Attachments:
POSTED BY: Ping-Chen Tsai
Answer
16 days ago

A problem that complicated can probably only be handled by FindRoot

POSTED BY: Frank Kampas
Answer
16 days ago

Group Abstract Group Abstract