Use the difference formula for tangent to simplify the expression. The formula states that <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>A</mi><mo>-</mo><mi>B</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>tan</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>+</mo><mi>tan</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>tan</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Remove parentheses.

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>15</mn><mi>π</mi><mo>)</mo></mrow><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>15</mn><mi>π</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>15</mn><mi>π</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>15</mn><mi>π</mi><mo>)</mo></mrow><mo>+</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>15</mn><mi>π</mi><mo>)</mo></mrow><mo>+</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Subtract full rotations of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> until the angle is greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and less than <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Subtract full rotations of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> until the angle is greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and less than <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mo>-</mo><mi>tan</mi><mrow><mo>(</mo><mn>2</mn><mi>t</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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