  Consider critical percolation in two dimensions. Under the condition that
there are k disjoint alternating black and white arms crossing the annulus
A(l,n), we prove a central limit theorem and variance estimates for the winding
angles of the arms (as n\rightarrow \infty, l fixed). This result confirms a
prediction of Beffara and Nolin (Ann. Probab. 39: 1286--1304, 2011). Using this
theorem, we also get a CLT for the multiple-armed incipient infinite cluster
(IIC) measures.
