Integral of sec^(2/3) x csc^(4/3) x from pi/6 to pi/3

The same question, asked 2 times: 13 May 2024 S2, 14 May 2024 S1. Every wording below, oldest first.

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Question 1
13 May 2024 S2
102 $\int_{\pi/6}^{\pi/3}\sec^{2/3}x\cdot\csc^{4/3}x\,dx$
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Question 2
14 May 2024 S1
114 $\displaystyle\int_{\pi/6}^{\pi/3}\sec^{2/3}x\cdot\csc^{4/3}x\,dx$
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