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$${most}\:{hated}\:{trigonometric} \\ $$$${problem}: \\ $$$$\mathrm{sin}\left(\:\frac{\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)=? \\ $$
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$$\boldsymbol{\mathrm{compute}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{double}}\:\boldsymbol{\mathrm{integral}} \\ $$$$\int_{\boldsymbol{\mathrm{y}}=\mathrm{0}} ^{\mathrm{1}} \int_{\boldsymbol{\mathrm{x}}=\mathrm{0}} ^{\mathrm{2}} \boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{dxdy}}\:\boldsymbol{\mathrm{and}}\:\:\int_{\boldsymbol{\mathrm{y}}=\mathrm{0}} ^{\mathrm{1}} \int_{\boldsymbol{\mathrm{x}}=\mathrm{0}} ^{\mathrm{2}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} \boldsymbol{\mathrm{dxdy}} \\ $$$$ \\ $$
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$${calculate}\:{the}\:{volume}\:{of}\:{a}\:{sphere} \\ $$$${using}\:{double}\:{integral} \\ $$
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