Solve Argument of sin \frac{8∏}{5} + i

[utkarshakash]

Homework Statement

$arg \left\{ sin \frac{8∏}{5} + i \left( 1 + cos\frac{8∏}{5}\right) \right\}$

Homework Equations

The Attempt at a Solution

$2sin \frac{4∏}{5} cos \frac{4∏}{5} + i2cos^{2} \frac{4∏}{5} \left(cos2θ=2cos^{2}θ-1 and sin2θ=2sinθcosθ\right)$

After simplification what is the next step?

 

[HallsofIvy]

Do you know what "argument" means in this problem?