Step 1 :Given a clockwise rotation of \(690^{\circ}\)
Step 2 :A full rotation is \(360^{\circ}\)
Step 3 :Since \(690^{\circ}\) is more than one full rotation, we need to find the remainder of \(690^{\circ}\) divided by \(360^{\circ}\)
Step 4 :The remainder is \(330^{\circ}\)
Step 5 :To find the counterclockwise equivalent, we subtract this remainder from \(360^{\circ}\)
Step 6 :The counterclockwise equivalent is \(30^{\circ}\)
Step 7 :\(\boxed{30^{\circ}}\) is the final answer