Add <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mfrac><mrow><mn>79</mn><mi>π</mi></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> .

Since the angle <math><mstyle displaystyle="true"><mfrac><mrow><mn>79</mn><mi>π</mi></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> is in the fourth quadrant, subtract <math><mstyle displaystyle="true"><mfrac><mrow><mn>79</mn><mi>π</mi></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>40</mn></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>40</mn></mrow><mrow><mn>40</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>40</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>79</mn><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>80</mn><mi>π</mi></mstyle></math> .

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